Full opinion text
LIPEZ, Circuit Judge. Table of Contents I Background .15 II The Consent Decrees.19 A. Background .19 1. Consent Decree I.19 2. Consent Decrees II, III, IV, and Capuano.20 3. The District Court Approval.20 B. • Reviewing the Approval of the Consent Decree.21 1. Standard of Review.21 2. Case or Controversy.21 3. Fairness.23 a. Procedural.23 b. Substantive.24 4. Reasonableness.25 5. Statutory Fidelity.26 6. Unconstitutional Taking.28 III The Declaratory Judgment.28 A. Background on CERCLA Contribution Actions.28 B. The District Court’s Declaratory Judgment Ruling.29 C. The Parties’ Challenges to the Declaratory Judgment.31 1. Proof that the Defendants Disposed of Hazardous Waste.31 a. Ashland .31 b. Acco-Bristol .34 c. Black & Decker a/k/a Gar.35 d. Perkin-Elmer.36 2. Wilbert Jones’s Testimony.37 a. Grounds for Exclusion.38 b. Grounds for Disbelieving.39 3. Exclusion of Master Chart.40 a. Procedural Posture .40 b. Admissibility of the Chart.41 4. Proof that Defendants’ Waste Caused or Contributed to Cleanup Costs.42 5. The Entry of a Declaratory Judgment under 42 U.S.C. § 9613(g)(2) and the Declaratory Judgment Act.45 6. Morton’s Liability.•.49 a. Claims of Clearly Erroneous Factual Findings.49 b. Claims of Legal Error.51 7. Successor-in-interest Liability for Gar.52 8. UTC’s Appeal.55 a. The Judgment in Favor of Macera.55 i. Transporter Liability.55 ii. Arranger Liability.58 b. The Judgment in Favor of the City of New Jersey.60 c. The Government’s $6 Million Enforcement Costs.61 IV Conclusion.63 Appendix I A Roster of Parties, Principals, and Witnesses .63 Appendix II A Summary of Relevant Monetary Sums .64 This appeal concerns the third phase of litigation under the Comprehensive Environmental Response, Compensation and Liability Act (CERCLA), 42 U.S.C. § 9601 et seq., stemming from the disposal of hundreds of thousands of gallons of hazardous waste in the late 1970s at a site in Smithfield, Rhode Island owned by William and Eleanor Davis. This phase concerns an action by United Technologies Corporation (UTC) under CERCLA’s contribution provision, 42 U.S.C. § 9613(f). In 1995, UTC was found jointly and severally liable for costs incurred by the United States for the cleanup of the Davis site. Hoping to relieve itself of some of the burden of that judgment, UTC sued several dozen other potentially responsible parties. Most of these parties, as well as UTC, signed partial consent decrees with the United States in which they agreed to pay a share of the cleanup costs. Several parties, however, did not settle, and in 1998 UTC took them to trial. One of the non-settlors, Ashland, Inc., appeals the district court’s entry of the partial consent decrees. Ashland and four other non-set-tlors also appeal the court’s entry following trial of a declaratory judgment holding them liable for disposing of hazardous waste at the Davis site and allocating to them shares of responsibility for cleanup costs. Finally, UTC appeals three aspects of the court’s ruling. We affirm, with one exception — a remand for clarification of the district court’s ruling that UTC may be solely responsible for $6 million in government enforcement costs. I. Background We describe the facts in the light most favorable to the judgment. During the 1970s, William Davis operated a waste disposal site on ten acres of land in Smith-field, Rhode Island. In 1982, the Environmental Protection Agency (EPA) placed the Davis site on its National Priorities List of hazardous waste sites. After undertaking a remediation investigation and completing a feasibility study, the EPA issued a Record of Decision in 1987 describing the cleanup work that it deemed necessary to mitigate the environmental damage caused by the hazardous waste disposal. As described by the EPA, the cleanup required the government to “(1) complete a water line to supply drinking water to areas where the drinking water wells already are contaminated and to areas where the contaminated groundwater plume threatens additional wells; (2) clean contaminated groundwater; and (3) excavate and clean contaminated soils that continue to contaminate the groundwater and other environmental media at the Site.” The EPA estimated the cost of this work at about $3 million for the water line, $13 million for groundwater cleanup, and $14 million for soil remediation. The government began the work of constructing water lines to nearby residents, but took no action on the soil or groundwater cleanups. See United States v. Davis, 11 F.Supp.2d 183, 192 (D.R.I.1998) (Davis II). In 1990, the United States brought an action under 42 U.S.C. § 9607 for recovery of past and future response costs at the Davis site. This provision of CERCLA allows the government to bring a “cost recovery action” against an owner or operator of a facility at which hazardous substances were disposed, against a transporter of hazardous waste, and against a party who arranged for the disposal or transport of hazardous waste. 42 U.S.C. § 9607(a). The government sued William Davis as an owner-operator; Eleanor Davis as an owner; United Sanitation, Inc. and A. Capua-no Brothers Inc. as transporters and arrangers; and Ciba-Geigy Corporation, Clairol Inc., Pfizer Inc., The Providence Journal Company, and UTC as arrangers. The district court trifurcated the government’s case. Phase I would determine whether the defendants were liable for response costs. Phase II would establish the amount of response costs incurred by the United States. Phase III, which is at issue in these appeals, would deal with all remaining claims, including claims for contribution, indemnification, and allocation of responsibility. In 1991, with the government’s case against it pending, UTC sued some of its co-defendants and 88 other companies under 42 U.S.C. § 9613(f), which allows one potentially responsible party (PRP) to bring an action for contribution against other PRPs. Some of these third-party defendants impleaded additional fourth-party defendants, bringing a total of 138 defendants into the litigation. The United States did not sue these parties directly. In a 1994 partial consent decree, Clairol Inc., Ciba-Geigy Corporation, Pfizer Inc., and The Providence Journal Company agreed collectively to pay the United States $5,625 million, plus interest accruing from the date of the settlement, toward the Davis site cleanup. UTC, however, did not settle, and the government took it to trial in 1995. After a bench trial, the district court found that UTC had dumped wax and solvent waste at the Davis site and held UTC jointly and severally liable for all past and future cleanup costs. See Davis I, 882 F.Supp. at 1225. While preserving the right to appeal that judgment, UTC stipulated that the response costs incurred by the EPA before September 30, 1987, and the enforcement costs incurred by the Department of Justice before September 30, 1994 — the cutoff dates set by the court for determining the government’s costs — totaled $9.1 million. See id. UTC and the United States also stipulated that the $5.8 million ($5,625 million plus interest) paid by the four set-tlors would be deducted from UTC’s liability. These stipulations eliminated the need for a Phase II trial. The case next proceeded to the Phase III claims for contribution, indemnification, and allocation of responsibility against the third and fourth-party defendants. By April 1996, the government said that it had incurred $19 million in response costs for site study and partial construction of waterlines and $6 million in litigation enforcement costs. See id. at 192. It projected future costs of $3 million to complete the water lines, $14 million for soil remediation, and $13 million for groundwater remediation, bringing the total response and enforcement costs at the site to $55 million. See id. In settlement negotiations, the government assigned PRPs to two groups according to their estimated share of liability, with settlement amounts based on the strength of the evidentiary case against each party. Eighty PRPs settled claims by joining one of five partial consent decrees, which also afforded the parties contribution protection against other PRPs. The first and largest of these consent decrees involved the United States, UTC, and 49 third and fourth-party defendants. See id. at 185. The parties agreed to pay $13.5 million plus $440,000 in oversight costs, of which UTC would pay $2.8 million. In addition, UTC agreed to perform the soil cleanup for the Davis site. While the cost of the soil work was estimated at $14 million, UTC agreed to accept the risk that the work might in fact cost more. UTC’s liability is reduced, however, by the other partial consent decrees, which provide for payments to UTC of up to $5,364 million. The district court approved the consent decrees in 1998 and 1999, finding them fair, both proeedurally and substantively, reasonable, and consistent with CERCLA’s objectives. Soil remediation efforts began in July 1997. United States v. Davis, 31 F.Supp.2d 45, 52 (D.R.I.1998) (Davis IV). To avoid recontamination, the groundwater cleanup will begin after the soil work is completed. Several defendants chose not to participate in any of the consent decrees. UTC prepared to try its claims for contribution against the non-settling defendants, including William Davis as owner and operator of the Davis site; Eleanor Davis as owner; Chemical Waste Removal (CWR), Chemical Control Corporation (CCC), and Mac-era Brothers Container Service, Inc. (Mac-era) as transporters; and Acco Bristol Division of Babcock Industries (Acco), Ashland Chemical, Inc. (Ashland), Gar Electroforming Division (Gar), a/k/a Black & Decker, Perkin-Elmer Corporation (PE), Thiokol, a/k/a/ Morton International Inc. (Morton), and the City of New Jersey as arrangers. Before trial began, the district court said that the trial would adjudicate UTC’s “request to determine the ‘equitable contribution share of liability’ for past and future response costs at the Site.” However, when UTC admitted at the start of trial that it had not begun to incur costs for soil remediation by the close of discovery, the court narrowed the trial’s focus to UTC’s right to contribution for future rather than past costs. It defined future costs as those that UTC had incurred since the close of discovery and those that it would incur as it completed the soil remediation. On September 28, 1998, following a 26-day bench trial, the court partially granted a motion for judgment made by some of the defendants based on partial findings pursuant to Federal Rule of Civil Procedure 52(c). The court ruled that while Macera had transported hazardous waste to the Davis site, it was not liable as a matter of law because UTC failed to prove that Macera “selected” Davis as a disposal site, as § 9607(a)(4) requires to hold a transporter of hazardous waste liable. See United States v. Davis, 20 F.Supp.2d 326, 334 (D.R.I.1998) (Davis III). The court also dismissed UTC’s case against the City of New Jersey, finding that the city was immune from liability under 42 U.S.C. § 9607(d)(2). Id. at 335. On December 15, 1998, the court issued a declaratory judgment holding appellants Ashland, Acco, Gar, Morton, and PE liable for arranging for the disposal of their waste at the Davis site. With the exception of Morton, the court allocated to each defendant a share of responsibility for UTC’s future cleanup costs. Davis IV, 31 F.Supp.2d at 69. The appeals currently before us result from the district court’s entry of the Phase III consent decrees, its rulings for some of the defendants pursuant to Rule 52(c), and its declaratory judgment in favor of UTC. Ashland appeals the district court’s approval of the consent decrees. Ashland, Acco, Gar, Morton, and PE appeal several aspects of the declaratory judgment. Specifically, four appellants (Ashland, Acco, Gar, and PE) argue that UTC failed to prove by a preponderance of the evidence that they arranged for the disposal of waste at the Davis site. These four appellants also argue that the district court abused its discretion by admitting and crediting the testimony of CWR driver Wilbert Jones. Acco and Gar also argue that the district court abused its discretion by excluding a “Master Chart” of the parties’ claims compiled by UTC’s lawyers to prepare the witness designated by UTC to testify on behalf of the corporation pursuant to Federal Rule of Evidence 30(b)(6). Three appellants (Ashland, Acco, and Gar) contend that UTC failed to prove by a preponderance of the evidence that their respective waste contained hazardous substances and so caused the incurrence of cleanup costs. These three appellants also argue that the court’s entry of a declaratory judgment was improper. Appellant Gar, a/k/a Black & Decker, challenges the court’s finding of corporate successor liability. Finally, UTC contests the court’s dismissal of the case against the City of New Jersey and Macera, and its ruling that UTC was solely responsible for $6 million in government enforcement costs incurred during Phase I and II of the litigation. We will discuss each of these challenges in turn. II. The Consent Decrees A. Background 1. Consent Decree I Ashland’s appeal focuses on Consent Decree I, the primary settlement between the United States and UTC, which began consent decree negotiations with the United States as an alternative to pursuing an appeal of the judgment in Davis I. In discussions with UTC, the EPA assigned possibly settling PRPs (generators and transporters of waste) to two groups, “carve-out” and “non-carve-out.” The carve-out entities were deemed primarily responsible for the waste at the Davis site, and so were compelled to negotiate individual settlements with the United States. Non-carve-out third parties were encouraged to negotiate a possible global settlement among themselves, with the assistance of liaison counsel. On July 14, 1995, following the Phase I settlement with four parties, the United States offered to settle with all remaining parties for about $16 million plus the performance of site soil cleanup using low-temperature thermal desorption technology. UTC provisionally agreed to the United States’s settlement offer and pursued its contribution claims. Ultimately, UTC, carve-outs Olin Hunt and American Cyan-amid, and about fifty other parties joined this settlement. The parties paid a total of $13.5 million to the United States, plus $440,000 in oversight costs. Of that amount, Olin Hunt and American Cyanam-id paid $2.75 million each (with some portion going to resolution of state claims), non-carve-out parties paid a total of $7.2 million, and UTC paid the remaining balance, about $2.8 million. Furthermore, UTC took responsibility for the entire expense of site soil remediation, an estimated cost of about $14 million. Under the settlement, UTC and the United States each receive half of future contribution recoveries, with UTC’s recovery capped at $5.364 million after deducting 15 percent of contribution recoveries for attorneys’ fees incurred in contribution litigation after March 1996. Finally, the settling parties received complete contribution protection from claims by other PRPs. Separate recoveries by the United States would not be subject to contribution sharing. While the predicted cost of cleaning up the Davis site has varied over the years, the most recent estimate, from 1997, took into account new remediation technology and set the total at $55 million. This amount guided the United States in determining the settlement amounts. In addition, the allocations to Clairol and the other parties in the earlier Phase I, $5,625 million settlement provided a “benchmark” for the amounts requested from potential settlors in the later consent decrees. Davis II, 11 F.Supp.2d at 191. 2. Consent Decrees II, III, IV and Capuano The remaining consent decrees included 27 additional parties and involved UTC’s settlement of claims for contribution from other PRPs, resulting in some additional payments to the United States pursuant to UTC’s agreement with the United States in Consent Decree I. In Consent Decree II, 23 parties paid a total of $4,135 million, with individual party liability detailed in briefs to the district court. Consent Decree III involved National Starch, which paid $5 million. Consent Decree IV involved a $150,000 payment by Swan Engraving and a $50,000 payment by Power Semiconductors. All parties to these settlements received complete contribution protection from future claims. Finally, Capuano Brothers paid $200,000 to the government, plus a like amount for settlement of cleanup costs at another Superfund site. 3. The District Court Approval To assist in its assessment of Consent Decree I, the district court held a two-day hearing to determine whether the proposed settlement was fair, both procedurally and substantively, reasonable, and consistent with CERCLA’s objectives. United States v. Cannons Eng’g Corp., 899 F.2d 79, 84 (1st Cir.1990). Procedurally, the court found that “[t]he negotiations were conducted openly and all parties were given an opportunity to participate.” Davis II, 11 F.Supp.2d at 189. Substantively, the court concluded that the consent decree met all requirements because the “proposed settlement reflects a rational method of allocating liability in a manner that reasonably approximates each party’s share of responsibility; the method is applied evenhandedly with respect to all PRP’s and sufficient information is presented to enable the Court to determine whether that has been done.” Id. at 192. In assessing the reasonableness of the consent decree, the court’s chief concern was “whether the public can be adequately compensated by a settlement in which the United States receives only a portion of the remediation cost from a party previously adjudged liable for the entire cost,” id. at 186, a reference to the release of UTC from the Phase I judgment. According to the district court, under the terms of the settlement the United States would receive $27.5 million, plus the $5.8 million from the original defendants, leaving a $21.7 million shortfall in compensation for the projected cost of the cleanup. This issue distinguished the Davis case from others in which the United States settled before judgment. “In those cases, compromising for a fraction of the response costs with a PRP that is potentially liable for the entire cost usually is justifiable on the ground that litigation might result in the United States recovering no response costs at all.” Id. at 192. The court thus framed the reasonableness question in terms of “whether the amount by which the judgment has been discounted reasonably reflects the risk of reversal [on appeal],” and called this “a very close question.” Id. at 193. The court acknowledged some “remaining, albeit diminished, litigation risk associated with the claim against UTC.” Id. The court also suggested that concern about releasing UTC from the judgment was mitigated by the fact that the United States could still sue the non-settlors for the $21.7 million shortfall, but recognized that this course of action seemed to involve “much greater litigation risk” than simply pursuing the judgment against UTC. Id. In resolving the issue, the court considered factors beyond an assessment of litigation risks. The court noted that “the financial obligations imposed on UTC are considerably greater than the obligations assumed by the other ‘carve-out’ settlors,” reinforcing UTC’s substantial responsibility. Id. It also noted that “given the deference accorded to the EPA’s judgment in such matters, it cannot be said that the proposed discount is unreasonable.” Id. The court said that the consent decree avoided an unduly harsh result for UTC, whereas the judgment would have “saddled [it], unfairly, with liability for remediation costs that far exceed its fair share.” Id. Acknowledging that UTC could pursue contribution actions against other PRPs, the court still concluded that the consent decree was reasonable given the great “difficulty of establishing entitlement to contribution.” Id. Finally, the court found the consent decree to be consistent with the statute because it advanced “the overriding goal of promptly and efficiently cleaning up hazardous waste sites.” Id. Pursuant to its thorough opinion, the district court approved Consent Decree I on February 13, 1998, and entered final judgment on December 9, 1999. Consent Decrees II, III, IV and the Capuano decree were each summarily approved subsequently. Final judgment was also entered on these decrees in December 1999. On appeal, Ashland, a non-settling PRP, lodges numerous objections to the approval of the consent decrees, including a jurisdictional objection. We assess these arguments. B. Reviewing the Approval of the Consent Decrees 1. Standard of Review Considerable deference is involved in the review of CERCLA consent decrees. Indeed, appellate review is “encased in a double layer of swaddling.” Cannons, 899 F.2d at 84. First, there is deference to the administrative agency’s construction of the settlement. “That so many affected parties, themselves knowledgeable and represented by experienced lawyers, have hammered out an agreement at arm’s length and advocate its embodiment in a judicial decree, itself deserves weight in the ensuing balance.” Id. Second, the appellate court can only review a district court’s approval of a consent decree for abuse of discretion, characterized by “a serious error of law” or a “meaningful lapse of judgment.” United States v. Charles George Trucking, 34 F.3d 1081, 1085 (1st Cir.1994); United States v. DiBiase, 45 F.3d 541, 544 (1st Cir.1995). “Because an appellate court ordinarily cannot rival a district court’s mastery of a factually complex case — a mastery often, as in this instance, acquired through painstaking involvement over many years — the district court’s views must also be accorded considerable respect.” Charles George, 34 F.3d at 1085. This double deference “places a heavy burden on those who purpose to upset a trial judge’s approval of a consent decree.” Cannons, 899 F.2d at 84. 2. Case or Controversy As a preliminary matter, Ashland contends that the district court had no jurisdiction under Article III to approve the consent decrees because, “with the exception of UTC, the U.S. never sued any of the third or fourth-party defendants settling in Consent Decrees I-IV. Moreover, approximately 34 entities who were signatories to Consent Decree I were never sued by any party to this action.” In Ashland’s view, this circumstance means that there was no “case or controversy” to be resolved by the district court. We conclude that, even if there were parties not sued by the United States involved in the consent decrees, their inclusion would be permissible because the Supreme Court has allowed unpleaded claims to be part of consent decrees, and thus, there is no “case or controversy” concern. In Local No. 93, Int’l Ass’n of Firefighters v. City of Cleveland, 478 U.S. 501, 525, 106 S.Ct. 3063, 92 L.Ed.2d 405 (1986), the Supreme Court ruled that a consent decree must (1) spring from and serve to resolve a dispute within the court’s subject matter jurisdiction; (2) come within the general scope of the case based on the pleadings; and (3) further the objectives of the law on which the claim is based. Although Firefighters involved a challenge to the scope of a consent decree rather than an Article III case or controversy argument, satisfying the criteria set forth in that case resolves any case or controversy claim. The district court found that the criteria were satisfied by Consent Decree I: The United States’s claims against the settling third and fourth-party defendants spring from and fall well within the scope of the controversy described in the pleading; ... Furthermore, the United States and all of the settling PRP’s are parties to the action and the consent decree resolves the dispute among them. Finally, ... approval of the consent decree also furthers the objectives of CERCLA by facilitating the prompt and efficient remediation of a major hazardous waste site. Davis II, 11 F.Supp.2d at 188. We have applied the Firefighters test in the CERCLA context before. In Charles George, we found that claims not expressly set out in the pleadings may be addressed in a consent decree as long as they fall within the pleadings’ general scope. 34 F.3d at 1089-91. Likewise, unpleaded claims that could not be brought against third-party defendants pursuant to a case management order (CMO) were appropriately included in the consent decree. Id. at 1091. Here, the purported failure to file complaints contemporaneous with the consent decrees does not defeat the legitimacy of the settlements. As we wrote in Charles George: [T]he Supreme Court has made clear that there is no per se prohibition against consent decrees that exceed the possible bounds of a decision issued directly by the trial court. Because a consent decree is animated not only by the parties’ legal claims but also by the parties’ consent, a court is “not necessarily barred from entering a consent decree merely because the decree provides broader relief than the court could have awarded after trial.” Id. at 1091 (quoting Firefighters, 478 U.S. at 525, 106 S.Ct. 3063). The district court allowed the inclusion of parties not sued by the United States in the consent decrees, finding that UTC’s contribution claims “are based on the same body of evidence and raise the same issues as the United States’ claims against the settling third and fourth-party defendants.” Davis II, 11 F.Supp.2d at 188. Like a settlement that is greater in scope than the originally pled claims, the inclusion of various third and fourth-party defendants, as well as interested non-parties, is permissible pursuant to Firefighters. Indeed, any conclusion to the contrary would disrupt the goals of CERCLA, which seeks early settlement with as many PRPs as possible to further expeditious remediation. 3. Fairness a. Procedural Assessing fairness in the CERCLA settlement context has both procedural and substantive dimensions. “To measure procedural fairness, a court should ordinarily look to the negotiation process and attempt to gauge its candor, openness, and bargaining balance.” Cannons, 899 F.2d at 86. The EPA has ample authority to structure its settlement negotiations, including “broad discretion to structure classes of PRPs.” Id. A finding of procedural fairness may also be an acceptable proxy for substantive fairness, when other circumstantial indicia of fairness are present. See Charles George, 34 F.3d at 1089. Ashland asserts that the consent decrees failed to meet the criteria of procedural fairness because the establishment of party categories inhibited the openness of negotiations; discovery relating to the settlement terms was inadequate; and the United States abdicated to UTC its responsibility to conduct the negotiations under CERCLA. Ashland also argues that information fundamental to evaluation of the consent decrees was not disclosed by the United States, including: (1) the United States’ total past and estimated future costs of remediation; (2) the strength of the United States’ case against each settlor; (3) the type, volume and toxicity of the waste for which each settlor was responsible and a correlation to site cleanup costs; (4) the formula by which the settlement amounts were calculated, and eviden-tiary support for the formula. These arguments are unpersuasive. All identified players in the hazardous waste site were notified of early opportunities for settlement with the United States, and later, with UTC. There is no reason to doubt that the consent decrees were the result of “arm’s length, good faith bargaining” between sophisticated parties. United States v. Comunidades Unidas Contra La Contaminacion, 204 F.3d 275, 281 (1st Cir.2000). PRPs were offered the assistance of a magistrate judge and an alternative dispute resolution administrator in the negotiation of their settlements. In addition, the early classification of carve-outs and non-carve-outs was an attempt at settlement management within the discretion of the United States. The district court also found no breach of the requirement for public disclosure, concluding that the parties offered “facts sufficient to enable one to determine whether” the terms of the agreement were fair. Davis II, 11 F.Supp.2d at 194. The proposed decrees lodged with the court “set[ ] forth, at length, all of the terms of the settlement.” Id. They were published in compliance with 42 U.S.C. § 9622(d)(2)(A)-(B), making the decrees available to non-parties and the public for comment in a timely manner. Furthermore, the district court noted that “there is no indication that the United States misrepresented or withheld any material facts.” Id. at 189. There is no error in any of these findings. Ashland’s argument that the identified information had to be available is not supported by the law, which makes significant allowances for gaps in information, given the sometimes impossible task of deriving this data. b. Substantive Substantive fairness involves concepts of corrective justice and accountability, concentrating on “the proposed allocation of responsibility as between settling and non-settling PRPs.” Charles George, 34 F.3d at 1088. “[T]he proper way to gauge the adequacy of settlement amounts to be paid by settling PRPs is to compare the proportion of total projected costs to be paid by the settlors with the proportion of liability attributable to them.” Id. at 1087. Ashland asserts that the formula used by the government to assess liability among the carve-out and non-carve-out parties, settling or not, was arbitrary and capricious, unrelated to comparative fault and inconsistently applied across consent decrees. The law on this issue is clear. The EPA formula should be upheld “so long as the agency supplies some plausible explanation for it, welding some reasonable linkage between factors it includes in its formula or scheme and the proportionate shares of the settling PRPs.” Cannons, 899 F.2d at 87. In assessing the formula applied, the quality of the information available to the government and settling parties informs the fairness analysis because data on the total extent of harm and the respective liabilities of various PRPs are often unavailable. See id. at 88. Such difficulties will not preclude a court from entering a consent decree. See Charles George, 34 F.3d at 1089. The calculation of liability and the allocation of that responsibility is specially within the scope of the Agency’s and parties’ expertise. “As long as the data the EPA uses to apportion liability for purposes of a consent decree falls along the broad spectrum of plausible approximations, judicial intrusion is unwarranted .... Having selected a reasonable method of weighing comparative fault, the agency need not show that it is the best, or even the fairest, of all conceivable methods.” Cannons, 899 F.2d at 88. In this case, the EPA assessed liability based on “its estimate of the volume of waste attributable to each PRP.” Davis II, 11 F.Supp.2d at 190. The EPA also considered the strength of the cases against the respective PRPs, taking “into account that there was direct and credible evidence linking some of the PRP’s to the Site and that the evidence with respect to other PRP’s was almost entirely circumstantial and varied in probative value.” Id. The district court found the interplay of these factors in this case to be “rational” and “especially appropriate in cases like this where the wastes have been intermingled and it is virtually impossible to attribute discrete portions of the cleanup costs to particular wastes.” Id. The court further observed that, in accord with the precedent, “assessing relative responsibility is an imperfect process because it requires subjective judgments based on evidence that is not completely developed and may be disputed. However, ... the evidence need not be exhaustive or conclusive in order to determine whether a proposed settlement is substantively fair.” Id. at 191. We agree with the district court’s analysis supporting the substantive fairness of the liability allocation among carve-outs and non-carve-outs, settlors and non-set-tlors alike. In arguments before the district court, the government attorney and others noted that the settlements involved “roughly half of the parties paying somewhat more than half of the costs.” In its decision, the district court stressed the parity of the amounts paid by settling PRPs and non-settling PRPs, both carve-outs and non-carve-outs. Davis II, 11 F.Supp.2d at 191. The court wrote: Comparing the amounts paid by the settling “carve-out” PRP’s to the Clairol benchmark and to the demands made upon the non-settling “carve-out” PRP’s supports the conclusion that the proposed settlement apportions liability in a manner that roughly approximates a rational. estimate of the relative responsibilities borne by both the settling and non-settling PRP’s. Id. at 190. The court proceeded to compare the settlement offered to American Cyanamid and Olin Hunt with the settlements paid in the Clairol agreement and demands made of eight non-settling carve-out PRPs, all of which fell between $2.75 million and $3 million. See id. at 191. Interestingly, the court also noted that the government demanded $8.25 million from the State of New Jersey, BFI and Ashland, averaging to a total of $2.75 million each, though Ashland “was expected to pay a larger share because EPA determined that Ash-land produced a high volume of hazardous waste and that a significant amount of evidence existed linking Ashland to the Davis site.” Id. at 191 n. 7. Finally, the court noted “an even closer correlation between the amounts paid by settling ‘non-carve-out’ PRP’s and the amounts demanded from non-settling ‘non-carve-out’ PRP’s” — $13.5 million demanded of eighty-five non-carve-out PRPs, averaging $158,800 apiece, compared with the $7.2 million proposed settlement with forty-seven non-carve-out PRPs, amounting to $152,200 each. Id. at 191. The court also pointed out that the allocation assessed to UTC was a considerably greater financial obligation than that imposed on any non-settling carve-out party. See id. In addition, the ultimate measure of accountability “is the extent of the overall recovery, not the amount of money paid by any individual defendant.” Charles George, 34 F.3d at 1086. Accordingly, a consent decree need not specify each generator’s or transporter’s degree of culpability. It is appropriate for classes of PRPs to be assigned aggregate settlement amounts to allocate among themselves. See id. In Charles George we said: “Realistically, a government agency, in the midst of negotiations, is in no position to put so fine a point on accountability. We, therefore, endorse, in general, EPA’s practice of negotiating with a representative group of PRPs and then permitting the group members to divide the burden of the settlement among themselves.” Id. Ashland’s challenge to the group allocations in these settlements is meritless. Our prior observation remains pertinent: “[A]s is true of consent decrees generally, they are built upon compromise and compromise in turn is a product of judgment.” Comunidades Unidas, 204 F.3d at 282. We agree with the district court’s conclusion that a “rational” method of allocating liability was “evenhandedly” applied. Davis II, 11 F.Supp.2d at 192. 4. Reasonableness In considering the'reasonableness of Consent Decree I, the district court addressed the novel issue of whether the public can be adequately compensated by a settlement in which the United States receives only a portion of the remediation cost from a party previously adjudged liable for the entire cost. See Davis II, 11 F.Supp.2d at 186. Arguing that adequate compensation is not possible under such circumstances, Ashland asserts that the consent decrees do not comport with the objectives of CERCLA. The assessment of reasonableness focuses on several elements: the effectiveness of the decree as a vehicle for cleaning the environment; providing satisfactory public compensation for actual (and anticipated) costs of remediation; and accounting for the relative strength of the parties’ litigating positions and foreseeable risks of loss. See Cannons, 899 F.2d at 89-90. In making these assessments, a court must once again allow for the agency’s lack of “mathematical precision,” as long as the figures derive from a plausible interpretation of the record. Id. at 90. Furthermore, effective remediation demands a more pragmatic meaning than whether the settlement meets a scientific ideal or approximates the projected costs of cleanup. See Charles George, 34 F.3d at 1085; United States v. Charter Int’l Oil Co., 83 F.3d 510, 521 (1st Cir.1996) (“A district court’s reasonableness inquiry, like that of fairness, is a pragmatic one.”); Comunidades Unidas, 204 F.3d at 281. Although the UTC allocation in Consent Decree I does not pay for the entire expense of the cleanup, UTC assumed the full cost of soil remediation (mitigated by contribution from later settlors), even if that estimated cost ultimately exceeds projections. Furthermore, the consent decrees staved off litigation risks associated with the settling parties, including a possible appeal by UTC of the judgment against it. See Davis II, 11 F.Supp.2d at 192. In addition, as the district court observed, “fundamental fairness prohibits the imposition of liability that is totally disproportionate to UTC’s share of responsibility.” Id. at 193. Discounts on maximum potential liability as an incentive to settle are considered fair and reasonable under Congress’s statutory scheme. See DiBiase, 45 F.3d at 546; see also Interim CERCLA Settlement Policy, Environmental Protection Agency, 50 F.R. 5034 (February 5, 1985). A PRP’s assumption of open-ended risks, such as the full cost of a component of the cleanup, may merit a discount. See Cannons, 899 F.2d at 88. Also, party-specific discounts may reflect the chances of the United States success in litigation against a given PRP. See id. It is appropriate “to factor into the equation any reasonable discounts for litigation risks, time savings, and the like that may be justified.” Charles George, 34 F.3d at 1087. The United States received a significant sum from the initial settlors, Consent Decree I settlors and contributions from set-tlors in Consent Decrees II-IV and Capua-no. Indeed, the United States fulfilled 60 percent of its $55 million claim through the consent decrees, including the earlier $5.625 million settlement with Clairol and other parties. The United States also retains the option of pursuing future cost-recovery actions against other non-settling PRPs. In light of the role of the consent decrees in expediting the remediation work, the substantial cost recovery by the United States, and the. strength of the cases against the various PRPs, we agree with the district court that the consent decrees met the test of reasonableness. 5. Statutory Fidelity The purposes of CERCLA include expeditious remediation at waste sites, adequate compensation to the public fisc and the imposition of accountability. “[I]t would disserve a principal end of the statute — achievement of prompt settlement and a concomitant head start on response activities — to leave matters in limbo until more precise information [is] amassed.” Cannons, 899 F.2d at 88; see also DiBiase, 45 F.3d at 545 (“[Settlements reduce excessive litigation expenses and transaction costs, thereby preserving scarce resources for CERCLA’s real goal: the expeditious cleanup of hazardous waste sites.”). Additionally, there is a “strong public policy in favor of settlements, particularly in very complex and technical regulatory contexts.” Comunidades Unidas, 204 F.3d at 280. Importantly, even though it was not obligated to do so, UTC began the process of remedial soil treatment in July 1997, well before the approval of Consent Decree I. This task included: excavation, removal and proper disposal of more than 1,000 drums of waste and 10,000 small jars, containers and vials; removal of more than 750,000 tires; and sampling and chemical analysis of over 65,000 cubic yards of soil. This head-start on repair of a hazardous waste site is the sort of good-faith cooperation that CERCLA seeks to encourage via settlement. To find this progress inadequate would frustrate the statute’s purpose. In asserting that the consent decrees are not faithful to the purposes of CERC-LA, Ashland focuses on the contribution protection afforded the parties to the consent decrees, fearing that a handful of non-settlors (i.e., Ashland and the other appellants), foreclosed from contribution actions because they did not join the consent decrees, could be held liable for a disproportionate share of the $21.7 million in as-yet unrecovered costs if the United States pursued them in cost recovery actions. CERCLA provides that “[a] person who has resolved its liability to the United States or a State in an administrative or judicially approved settlement shall not be liable for claims for contribution regarding matters addressed in the settlement.” 42 U.S.C. § 9613(f)(2); see also 42 U.S.C § 9622(f)(2). Despite this “matters addressed in the settlement” language of the statute, Ashland says that the “matters addressed” language of the decrees here is overreaching because they include, quoting the consent decrees, “response costs incurred and to be incurred by any person or entity other than the United States for response actions related to the site or identified in the remedy.” Ashland complains that, “[a]s written, the ‘matters addressed’ provision of three partial consent decrees have been expanded to include all costs, whether the costs are incurred by the U.S. or by a private party. This is clearly impermissible under CERCLA.” Facing exposure to performance of the groundwater remedy, which may represent 40 percent of the total site costs, Ashland worries that parties like itself will bear disproportionate liability because they are unfairly barred from seeking contribution from earlier-settling parties. The practice of encouraging early settlements by providing broad contribution protection is provided by statute. 42 U.S.C. § 9613(f)(2); see also Charter, 83 F.3d at 522; UTC v. Browning-Ferris Ind., Inc., 33 F.3d 96, 103 (1st Cir.1994) (“This paradigm is not a scrivener’s accident.”). CERCLA also seeks to induce settlements at higher amounts by allowing settlors to seek contribution from those who have not yet settled. See 42 U.S.C. § 9613(f)(3)(B); Charter, 83 F.3d at 522. Still, EPA policy encourages the court reviewing a consent decree incorporating contribution protection to seek “a demonstration that this result is fair to potential contribution plaintiffs whose rights would be extinguished.” DOJ/EPA Memorandum, Defining “Matters Addressed” in CERCLA Settlements, March 14, 1997. In a case such as this, where UTC assumes an open-ended cost for soil remediation, and takes the lead in coordinating settlements and beginning the cleanup effort, the benefit of contribution protection is appropriate. Also, as UTC points out in its brief, Ashland’s preoccupation with the potential of disproportionate liability “ignores the fact that UTC, which was allocated responsibility for 1.54 percent of the liability by the trial court, will perform the source control remedy, which will amount to over one-fourth of the total costs of remediating the site.” UTC draws from this fact an appropriate conclusion: “This comparison shows that CERCLA can impose harsh results on PRPs; it also shows that these contribution defendants [Ash-land and other non-settlors] may bear a burden roughly comparable to that of UTC.” The point we made in an earlier decision remains apt: “As to the extinguished contribution claims of non-settlors or later round settlors, protection against those claims was a reasonable benefit [the set-tlor] acquired in exchange for settling before those others.” Charter, 83 F.3d at 522. The result of non-settlors possibly bearing disproportionate liability for the open-ended cost of remediation is therefore consistent with the statute’s paradigm, which encourages the finality of early settlement. See Browning-Ferris, 33 F.3d at 103. 6. Unconstitutional Taking To the extent that CERCLA authorizes the contribution protection to which Ashland objects, Ashland asserts that this protection could result in an unconstitutional taking of the protectable property interests of non-settling parties because they will be prohibited from seeking contribution from earlier-settling parties. Indeed, Ashland points out, CERCLA recognizes that in a settlement “limiting any person’s right to obtain contribution from any party,” the result could be “a taking without just compensation” under the Fifth Amendment. 42 U.S.C. § 9657. Ashland’s argument in support of this takings claim is so perfunctorily developed that we deem it unworthy of response. See United States v. Zannino, 895 F.2d 1, 17 (1st Cir.1990) (“[I]ssues adverted to in a perfunctory manner, unaccompanied by some effort at developed argumentation, are deemed waived.”). In support of its takings argument, set forth in two-and-a-half pages at the end of an 85-page brief, Ashland relies entirely on a brief description of the recent Supreme Court decision in Eastern Enterprises v. Apfel, 524 U.S. 498, 118 S.Ct. 2131, 141 L.Ed.2d 451 (1998), a case in which a deeply divided Supreme Court struck down retroactive application of the Coal Industry Retiree Health Benefit Act of 1992. The takings analysis put forth by the plurality opinion in that case did not command a majority of the Court, a fact which, as the government notes in its brief, severely limits the precedential value of that takings analysis. See Hertz v. Woodman, 218 U.S. 205, 213-14, 30 S.Ct. 621, 54 L.Ed. 1001 (1910) (“[T]he principles of law involved not having been agreed upon by a majority of the court sitting prevents the case from becoming an authority for the determination of other cases, either in this or in inferior courts.”). As Justice Kennedy noted in his concurring opinion in Eastern Enterprises, where he disavowed the takings analysis of the plurality: “Cases attempting to decide when a regulation becomes a taking are among the most litigated and perplexing in current law.” 524 U.S. at 541, 118 S.Ct. 2131. We will not assay the takings issue on the basis of the insubstantial argument put forth by Ashland. III. The Declaratory Judgment A. Background on CERCLA Contribution Actions When an innocent party, usually the government, brings a cost recovery action under § 9607, CERCLA imposes strict liability for the costs of cleanup on a party found to be an owner or operator, past operator, transporter, or arranger. See Acushnet Co. v. Mohasco Corp., 191 F.3d 69, 74 (1st Cir.1999). A party found liable under § 9607 may in-turn bring an action for contribution against other polluters under § 9613(f). In other words, while CERCLA allows for full recovery of costs from a party sued successfully under § 9607, it also permits that party to seek contribution from other parties that have helped create a hazardous waste problem. See Control Data Corp. v. S.C.S.C. Corp., 53 F.3d 930, 936 (8th Cir.1995). The statute thus provides that a court may, in its discretion, “allocate response costs among liable parties using such equitable factors as the court determines are appropriate.” 42 U.S.C. § 9613(f). As the Ninth Circuit has said, “[a] PRP’s contribution liability will correspond to that party’s equitable share of the total liability and will not be joint and several.” Pinal Creek Group v. Newmont Mining Corp., 118 F.3d 1298, 1301 (9th Cir.1997). The standard for contribution liability is the same as the standard for cost recovery liability. See Acushnet, 191 F.3d at 75. A plaintiff seeking contribution under § 9613(f) must prove that (1) the defendant falls within one of the four categories of covered entities (i.e. is a current or past owner or operator, a transporter, or an arranger); (2) a “release or threatened release” of hazardous waste involving the defendant’s facility occurred; (3) the release or threatened release caused the incurrence of response costs by the plaintiff; and (4) the plaintiffs costs were “necessary costs of response ... consistent with the national contingency plan.” 42 U.S.C. § 9607. B. The District Court’s Declaratory Judgment Ruling The district court found that UTC had unquestionably proven that the Davis site was a hazardous waste facility, that a release of hazardous waste had occurred, and that this release caused the incurrence of response costs because of the necessary cleanup. The court thus focused on the only remaining issue for CERCLA liability: “[W]hether the defendants are liable for those response costs on the grounds that they either operated the facility, transported the hazardous substances to the site, or arranged for the hazardous substances to be disposed of at the Site.” Davis IV, 31 F.Supp.2d at 61. Since each of the appellants was found to be an arranger, we focus on that aspect of the court’s ruling. The court began by considering the evidence that CWR, the Bridgeport, Connecticut waste transport company used by Ashland, Acco, Gar, and PE, disposed of waste at the Davis site. The court found that in 1977, “all of CWR’s waste was taken, initially, to Sanitary Landfill,” another Rhode Island disposal site, but that sometime after May 1977, Anthony and Jack Capuano, owners of Sanitary Landfill, began diverting some of CWR’s waste to the Davis site. Id. at 53. Based on receipts kept by William Davis and offered into evidence by UTC, the court found that “the Capuanos directed CWR drivers to the Davis Site on fifteen separate occasions.” Id. The Davis receipts show that these CWR deliveries took place between May 13 and July 7. The court said that CWR had two drivers, Wilbert Jones and Johnny Granfield, who collected 55-gallon drums of waste from customers. Both Jones and Gran-field sometimes drove a 40-foot flatbed truck that carried a full load of 79 drums and was “used to haul drums to Rhode Island.” Id. at 52-53. Based on the testimony of Jones and of Emanuel and Michael Musillo, the principals of CWR, the court made findings about CWR’s pickup and disposal practices: If a full load was collected early in the day, the drums, sometimes, would be taken directly to Sanitary Landfill. Usually, however, the truck would return to CWR, and the load of drums would be taken to Sanitary Landfill on the following day. If less than a full load was collected, the drums would be kept at CWR until seventy-nine drums had accumulated. Those drums then would be loaded onto the flatbed and driven to Sanitary Landfill. Drums were collected with such regularity that they never remained on CWR’s premises for more than three days. Id. at 53. Following the theory that CWR disposed of waste within three days of collecting it from a customer, the district court matched the dates of CWR waste pickups from appellants Ashland, Acco, Gar, and PE to the dates of waste deliveries to the Davis site. CWR kept bills of lading that recorded the dates on which it picked up wastes from customers. Some of the appellants kept parallel invoices. William Davis’s receipts included the dates of waste deliveries. Based on this evidence, the district court determined when an arranger’s waste was picked up within three days of a delivery to the Davis site. The court then concluded that it was “reasonable to infer” that this waste was in fact disposed of at the Davis site. Id. at 56. For example, the court held Ashland liable for a 79-drum load that CWR picked up from Ashland on June 1, 1977 because a Davis receipt showed that CWR driver Wilbert Jones delivered 79 drums to Davis on June 2. Id. The court next turned to allegations that transporter CCC, the company used by Morton, disposed of waste at the Davis site. The court found that CCC made 47 trips to the Davis site between May 1977 and the first week of July and that Morton’s waste was included in some of those deliveries. Id. at 55. Finally, the district court allocated responsibility for cleanup costs that UTC had incurred or would incur in completing the soil remediation. The chief factor in the court’s determination was the volume of waste disposed at the Davis site that could be attributed to each defendant based on the evidence about specific deliveries. Davis IV, 31 F.Supp.2d at 64. For example, the court found that CWR made two 79-drum deliveries containing 8,690 gallons of Ashland’s waste to the Davis site, and so allocated to Ashland a share of responsibility for cleanup costs based on that volume. Id. at 67. Based on its calculations of waste volume, the court allocated 1.03 percent of UTC’s future cleanup costs to Ashland, .16 percent to Acco, .03 percent to Gar, and .57 percent to PE. Id. at 69. The court also allocated 1.54 percent of responsibility to UTC. Id. Because the court found no evidence of specific deliveries yielding data about the volume of Morton waste disposed, it did not allocate a share of future cleanup costs to Morton. Id. at 65. C. The Parties’ Challenges to the Declaratory Judgment 1. Proof that the Defendants Disposed of Hazardous Waste We review the district court’s factual findings pursuant to a clear error standard. See Dedham Water Co., Inc. v. Cumberland Farms Dairy, Inc., 972 F.2d 453, 457 (1st Cir.1992). Clear error review means that: Findings of fact will be given effect unless, after reading the record with care and making due allowance for the trier’s superior ability to gauge credibility, the reviewing court form [sic] a strong, unyielding belief that a mistake has been made.... The same high level of respect attaches whether the conclusions of the trial court depend on its election among conflicting facts or its choice of which competing inferences to draw from undisputed basic facts. Id. (internal quotation marks omitted). Importantly for this case, “[w]hen the evidence supports conflicting inferences, the district court’s choice from among the several inferences cannot be clearly erroneous.” Id. at 462. We also note that findings of fact, even if brief, are sufficient as long as they permit a clear understanding of the grounds for the decision below. See Applewood Landscape & Nursery Co., Inc. v. Hollingsworth, 884 F.2d 1502, 1503 (1st Cir.1989). With those standards in mind, we address each party’s claims separately. a. Ashland In 1977, Ashland operated a chemical manufacturing plant in Great Meadows, New Jersey, generating waste that contained nitrating acid, sulfuric acid, nitric acid, and solvents composed of isopropyl alcohol, methyl alcohol, toluene, benzene, and xylene. It is undisputed that Ashland contracted with CWR to dispose of this waste, and the record supports the district court’s finding that CWR transported waste to the Davis site. While Michael Musillo of CWR testified that between 1975 and 1977 the company took all of its waste initially to the Sanitary Landfill owned by the Capuanos, Jack Capuano testified that after April 1977, when the landfill began getting complaints about odor, his brother Anthony Capuano began diverting some of CWR’s waste to the Davis site. CWR’s pickup slips and billing records, as well as Ashland’s disposal logs, show that during May and June of 1977, CWR picked up thirteen tanker loads and four flatbed loads from Ashland. Each of the flatbed loads contained 79 55-gallon drums. One of the flatbed pickups took place on June 1 and another occurred on June 30. Davis receipts bearing the name “Capuano,” signed by Wilbert Jones, and recording 79-drum loads, show that CWR deliveries were diverted from Sanitary Landfill to the Davis site on June 2 and July 5. Based on its theory that CWR delivered its waste within three days of accumulating a full flatbed load, and the explanation that the intervening weekend and July 4th holiday accounted for the five-day gap between June 30 and July 5, the district court found Ashland liable for the waste that CWR delivered to the Davis site on June 2 and July 5. There is evidence in the record to support the court’s conclusion. Emanuel Mu-sillo, principal of CWR, testified that when a driver picked up a full 79-drum load early in the day, he would go straight to Rhode Island to dispose of it. When a driver picked up a full load late in the day or picked up only a partial load, he would park the load at CWR overnight. The next day the driver would either continue to Rhode Island if the truck was full, or collect waste from another customer if it was not. While Musillo did not definitively testify that CWR always delivered waste within three days of collecting it, he said that when a driver accumulated a full 79-drum load, the drums would be taken to Rhode Island “within a few days, I would imagine.” CWR driver Wilbert Jones also testified that after picking up a complete load, he would leave it at CWR overnight and then leave for Rhode Island early the next morning. Ashland challenges the court’s factual findings on several grounds. Ashland begins by pointing out that UTC presented no direct evidence, such as drums or other containers bearing Ash-land’s name and found at the Davis site, to show that Ashland’s waste was on the CWR deliveries to the Davis site. While Ashland is correct, direct evidence is not a prerequisite to proving the elements of liability in a contribution action. See 42 U.S.C. § 9613(f) (setting forth elements of liability). To attack the district court’s finding that CWR disposed of waste within three days of collecting it, Ashland offers alternative scenarios. Ashland’s most plausible theory is based on Jones’s testimony that the Musillos sometimes “offloaded” nonflammable liquid waste by pouring it from drums into a tanker truck or underground storage facility at CWR. Ashland argues that its waste thus was likely unloaded at CWR’s Bridgeport site after pickup and either mixed with other waste or stored there for an indefinite period. Additional testimony by Jones and the Musillos calls this theory into question. Jones was asked this question: “[L]et’s suppose that you brought back some drums from one or more customers to Bridgeport, and that" you offloaded those drums. Let’s say it wasn’t a full load. Typically, how long would it take before those offloaded drums would find then-way to Rhode Island to be dumped?” Jones answered: “No more than three days.” Jones also said that the Musillos, not he, did most of the mixing work. Emanuel Musillo testified that offloading was not CWR’s normal practice because of the “double work” involved. He said that when drums were offloaded, they usually contained waste oil that CWR could resell. Musillo also said that occasionally other kinds of waste were stored at CWR, but only until the next delivery trip to Rhode Island. Michael Musillo corroborated aspects of his brother’s account. In light of this testimony, the district court did not err in finding that it was more likely than not that the waste CWR collected from Ashland on June 1 and June 30 was the waste the transporter delivered to the Davis site on June 2 and July 5. Since both pickups from Ashland were full 79-drum loads, it seems particularly unlikely that CWR drivers would have taken a full load off the flatbed truck on one day, only to deliver a full load of different drums to the Davis site on the next business day. Ashland’s alternative scenarios are simply “competing inferences” that the district court chose not to draw. Dedham Water, 972 F.2d at 457. Such