The plaintiffs, owners of industrial property in Malden, filed a complaint seeking damages from the defendant pursuant to G. L. c. 21E, the Massachusetts Oil and Hazardous Material Release Prevention Act, for contamination of their property by the defendant’s corporate predecessor. See Black v. Coastal Oil New England, Inc. (Black I), 45 Mass. App. Ct. 461, 461-462 (1998). Following a bench trial in the Superior Court, judgment was entered awarding the plaintiffs $13,320.39 for response costs under G. L. c. 21E, § 42; $2,190,000 for damage to their realty under G. L. c. 2IE, § 5; and $246,035.48 in attorney’s fees and costs under G. L. c. 21E, § 15. Id. at 462. After an appeal by the defendant, we affirmed the portion of the judgment for response costs under § 4; reversed the portion of the judgment for damage to the realty under § 53; vacated the award of attorney’s fees and costs under § 15; and remanded the case so that there could be a new determination of attorney’s fees and costs to be awarded in light of the reversal regarding § 5 damages. Id. at 468. We concluded that “the plaintiffs are entitled to recover, pursuant to § 15, all costs and attorney fees related to their proof and recovery of § 4 response costs incurred by them. Because the record is not susceptible of separating the § 4 costs and fees from those incurred with respect to § 5, the matter of the plaintiffs’ entitlement under § 15 must be resolved by the Superior Court.” Ibid.
On remand, a judge of the Superior Court4 rejected the defendant’s contention that G. L. c. 21E, § 15, required a proportionality between a plaintiff’s recovery and the fees *698awarded/ so that a fee award in this case could not exceed the $13,320.39 recovered by the plaintiffs under § 4. Concluding that a recovery under § 4 required that a plaintiff prove that the defendant' was a “person hable” under § 5(a), see Mailman’s Steam Carpet Cleaning Corp. v. Lizotte, 415 Mass. 865, 873-874 (1993), and applying the criteria of Linthicum v. Archambault, 379 Mass. 381 (1979),* ***5 the judge found that the time expended by plaintiffs’ counsel was fair and reasonable (with an exception not relevant to this appeal) with respect to the recovery of § 4 damages6; isolated that portion of the fees and costs attributable to § 5 claims; and entered no awards for the latter. Accordingly, he ordered that the defendant pay the following amounts: $157,752 in attorney’s fees; costs of $10,036; and expert witness fees of $14,556.14, for a total award under § 15 of $182,344.14.
On appeal, the defendant concedes that “proportionality” of recovery and fees under G. L. c. 21E, § 15, is not mandatory. Rather, the defendant argues that the concept of “reasonableness” applicable to fee awards must embrace factors beyond merely those set forth in Linthicum.7 Here, the defendant contends, the judge should have taken into account that (1) the plaintiffs pursued a meritless claim under § 5; (2) prosecution of that claim resulted in the incurring of significant legal expense by the defendant; and (3) the plaintiffs themselves violated the statutory scheme under which they sought relief (i.e., the Massachusetts Contingency Plan). Had these factors been taken into consideration, the defendant continues, “reasonable” fees and costs, see G. L. c. 21E, § 15, as inserted by St. 1986, c. 554, § 3, would represent no more than a small por*699tian of the total amount recovered by the plaintiffs on their § 4 claims. We agree with the analysis of the remand judge, and accordingly affirm.
1. Issue preclusion. Initially, we address the plaintiffs’ claim that this appeal is barred by the doctrine of issue preclusion. The plaintiffs point to the statement in our earlier decision, see Black I, supra at 468, that they are entitled to recover “all costs and attorney fees related to their proof and recovery of § 4 response costs incurred by them.” They argue therefrom that we have already adjudicated the contention, on which the defendant’s appeal is based, that reasonableness requires a reduction in awardable fees and costs.
“The doctrine of issue preclusion prevents relitigation of an issue determined in an earlier action when the same issue arises in a later action, based on a different claim, between the same parties or their privies, and the determination was essential to the decision on the earlier action.” Salem v. Massachusetts Commn. Against Discrimination, 44 Mass. App. Ct. 627, 639 (1998). We do not find that the defendant’s proposition was in any way determined in the earlier decision. What was before the court was the question of an existing fee award rendered irrelevant by a reversal of a portion of the judgment on which that fee award was based. This necessitated a redetermination of fees and costs to be awarded in light of the conclusion that the plaintiffs were entitled to fees with respect to their claims under § 4, but not with respect to their claims under § 5. We intended no subliminal messages to the remand judge regarding what he should or should not do regarding determination of the award applicable to the § 4 claims. There has been no issue preclusion.
2. Reasonable fees and costs under G. L. c. 21E, §15. On remand, the defendant appears to have argued that (1) the hours expended by the plaintiffs’ counsel were excessive; and (2) regardless of the reasonableness per se of the hours expended, there must be a “proportionality” between the amount recovered and the fees and costs awarded. The judge found that the time expended by the plaintiffs’ counsel was reasonable, given the need for discovery of facts from three decades earlier; the need for expert analysis and testimony; fourteen days of trial; and success in establishing the defendant’s responsibility for the *700contamination and the existence of response costs recoverable under § 4. The defendant, having chosen to litigate its liability for the contamination, is scarcely in a position to object to a reimbursement to the plaintiffs of expenses reasonably required to establish that liability. The judge appropriately exercised his discretion in deciding what constituted reasonable fees for these purposes in the light of the authorization of G. L. c. 21E, § 15, that fees may be awarded to a party, other than the Commonwealth, “who advances the purposes of this chapter.” See Sanitoy, Inc. v. Ilco Unican Corp., 413 Mass. 627, 633 (1992). The judge was also warranted in concluding that all fees and costs attributable to § 5 claims had been identified and excluded from the § 4 fee and cost award. Likewise, the judge correctly ruled that proportionality predicated on the amount recovered is not a requirement. This issue was laid to rest in Sanitoy, supra.
On appeal, the defendant veers off somewhat from the proportionality argument presented to the remand judge, advancing here the concept that the award of fees and costs under § 15 should be framed in a way that gives consideration to the allegedly baseless claim of the plaintiffs under § 5, as well as to their violation of the requirements of the Massachusetts Contingency Plan. Arguably, because the defendant apparently did not present its argument in this form to the remand judge, we would be justified in declining to address it. However, we think it is sufficiently embraced within the proportionality proposition to protect it from a charge of waiver, and we prefer to address the contention on the merits. We conclude that the judge correctly rejected the defendant’s assertion.
General Laws c. 21E, § 15, provides that “[i]n any suit by Massachusetts residents to enforce the requirements of this chapter, or to abate a hazard related to oil or hazardous materials in the environment, the court may award costs, including reasonable attorney and expert witness fees, to any party other than the commonwealth who advances the purposes of this chapter.” The statute applies to-actions for reimbursement. Sanitoy, Inc. v. Ilco Unican Corp., supra at 631-633. We discern nothing in the statute, or in the cases that have construed it, that *701calls for an offset against otherwise reasonable and recoverable fees and costs because the case contained other claims on which the plaintiffs did not prevail (or, given the statutory basis for authorizing fee-shifting, because there were claims that did not advance the purposes of G. L. c. 21E).8 To the extent that the plaintiffs violated requirements of the Massachusetts Contingency Plan, they have been penalized already by a reduction in the damages available to them under § 49; there is no logic in penalizing them again in the form of a reduced fee award. Even were we to assume that the plaintiffs’ claims under § 5 were baseless,10 a remedy is found in G. L. c. 231, § 6F, providing relief in the event of frivolous claims, or in Mass.R.Civ.P. 11(a), 365 Mass. 753 (1974), providing relief for unsupported pleadings. That remedy does not resurface to reduce fees and costs which a party would otherwise be awarded.
3. Appellate fees and costs. We conclude that G. L. c. 21E, § 15, authorizes the awarding of appellate fees and costs to a prevailing private party. See Yorke Management v. Castro, 406 Mass. 17, 19-20 (1989). In order to advance the purposes of c. 21E, the Legislature has provided for fee-shifting. It could not have been the Legislature’s intention that a party incur unreimbursable expenses in order to retain in appellate litigation a fee award that has already been rendered. The plaintiffs may ap*702ply for an award of appellate fees and costs by following the procedures set forth in the Yorke Management decision.
Judgment after remand affirmed.