243 F.3d 25 (1st Cir. 2001)
NORTHEAST DRILLING, INC., Plaintiff, Appellee,v.INNER SPACE SERVICES, INC.; NATIONAL GRANGE MUTUAL INSURANCE COMPANY, Defendants, Appellants,v.RANGER INSURANCE COMPANY, INC. Counterclaim Defendant, Appellee.
No. 00-1684
United States Court of Appeals For the First Circuit
Heard December 4, 2000Decided March 16, 2001

APPEAL FROM THE UNITED STATES DISTRICT COURT FOR THE DISTRICT OF MAINE
[Hon. D. Brock Hornby, U.S. District Judge] [Copyrighted Material Omitted][Copyrighted Material Omitted]
Richard L. Neumeier, with whom Timothy J. van der Veen and McDonough, Hacking & Neumeier, LLP, were on brief, for appellants.
Deirdre M. Smith, with whom Jerrol A. Crouter and Drummond Woodsum & MacMahon, were on brief, for appellees.
Before Selya, Circuit Judge, Stahl, Circuit Judge, and Lisi,* District Judge.
STAHL, Circuit Judge.


1
During the construction of a shipbuilding facility in Bath, Maine, a series of events, primarily attributable to the caprices of nature, delayed the schedule, forcing significant alterations to the work plan and ultimately making the project more expensive than had been anticipated. These events led to a dispute between the project's dredging subcontractor, Inner Space Services, Inc. ("ISSI"), and the drilling and blasting subcontractor it had hired, Northeast Drilling, Inc. ("NDI"), over who should bear the additional costs arising from these various matters. Following a six-day bench trial, the district court determined that NDI should receive some of the payments it claimed were due under its contract with ISSI, but that it was not entitled to the full amount because it had failed to render complete performance under its agreement with ISSI. The court also awarded attorney's fees and interest to NDI.


2
On appeal, ISSI challenges a number of the district court's factual findings, and argues that the court erred by declining to make certain additional findings. ISSI also assigns error to several legal determinations made by the district court, including the district court's failure to join the general contractor as a party, its refusal to grant ISSI's motion for judgment as a matter of law, and its approach to calculating damages. We affirm in all respects.

I. Background

3
The facts of this case are chronicled extensively in the district court opinion, Northeast Drilling, Inc. v. Inner Space Servs., Inc., No. 99-173-P-H, 2000 WL 761020 (D. Me. Mar. 31, 2000), and so we restrict our discussion to the facts bearing on this appeal. On September 21, 1998, ISSI, a Massachusetts-based firm, entered into an agreement with Atkinson Construction ("Atkinson"), the general contractor on the Bath Iron Works Land Level Facility Construction Project ("BIW Project" or "Project"). The BIW Project, which took place along the banks of the Kennebec River in Bath, Maine, involved the creation of a fifteen-acre facility enabling Bath Iron Works to build simultaneously three Navy destroyer ships and to launch those ships into a floating dry dock. To this end, ISSI was hired by Atkinson to lower the underwater rock table to a suitable elevation through drilling, blasting, and dredging.


4
Before submitting its bid to Atkinson, ISSI had contacted NDI, a drilling and blasting specialist headquartered in Maine, about NDI's availability to perform work on the BIW Project. After securing the subcontract with Atkinson, ISSI concluded an agreement with NDI on November 2, 1998. According to the terms of the ISSI-NDI contract, NDI was to be paid $1,140,000 for its drilling and blasting work on the area of submerged rock specified in the Atkinson-ISSI contract.1 For this sum, NDI agreed to perform blasting on a "6 x 6 grid, with the intent of supplying 'diggable' rock for dredging."2 Nowhere in the contract was the term "diggable" defined. The agreement further provided that if, at some point during the Project, ISSI asked NDI to perform drilling and blasting work outside of the designated area in order to achieve the desired elevation therein, NDI would receive a "proportional amount of any claims made to Atkinson by ISSI" for such additional work. Pursuant to the parties' arrangement, NDI was to be paid "if and only if ISSI receives compensation" from Atkinson for work in this "expanded" area.3 Finally, the timeline for NDI's performance under the contract was structured to account for the stringent environmental regulations protecting the Kennebec River's sturgeon population. NDI was to commence work on or about November 15, mid-November being the point at which the sturgeon typically vacate the affected area, and was to finish its operations by the end of March of the following year, when the fish were expected to return.


5
Unfortunately for the parties, the Kennebec River sturgeon were uncharacteristically slow to swim away from the Project area that year and, as a result, NDI did not receive authorization to begin blasting until January 7, 1999. By that time, ice floes had emerged on the surface of the river. This floating ice posed a significant challenge to NDI's operations by threatening to detach the detonation cords that NDI planned to stretch from the drilling barge to the holes in the submerged rock that contained the blast charges. In response to this problem, NDI abandoned its original blasting plan, which called for detonating several rows of explosives simultaneously, and decided to blast one row at a time. This attempt at problem-solving only created a new set of difficulties, however, as the blasting of the first row of charges broke up the rock in the surrounding area, making it nearly impossible to fulfill the contractual obligation to drill another row of holes six feet from the previous row. Accordingly, NDI proposed an alternative to ISSI: it would extend the size of the drilling and blasting grids from 6' x 6' to 6' x 7' or 6' x 8' while continuing to blast one row at a time. ISSI was reluctant to endorse this enlarged-pattern approach, as it knew that its likely byproduct would be larger pieces of rock that would be more difficult to dredge, and it expressed these concerns, in writing and in person, to NDI's president, Forrest Bradbury. Nonetheless, NDI went forward with the modified plan, believing that it had secured ISSI's acquiescence.


6
The ad hoc nature of this drilling and blasting technique also forced the parties to incur unexpected costs along the way. In order to account for the extra labor necessitated by the single-row, enlarged-grid blasting technique, Atkinson leased an additional drilling barge, known to the parties as the "Hughes barge," and backcharged its cost to ISSI. ISSI, in turn, deducted this cost from the amount to be paid to NDI. Additionally, NDI was called upon by ISSI to do drilling and blasting in the "expanded" area in an attempt to improve the quality of the blasted rock inside the contract area. ISSI, however, failed to submit a change-order request to Atkinson, as required under its agreement with the general contractor, until September 1999 -- nearly six months after NDI had demobilized from the BIW Project site.


7
Although NDI ultimately did complete its drilling and blasting work before the March 31 environmental window closed, the proportion of large rock it left behind made it impossible for ISSI to do dredging work using the equipment already on site.4 This forced ISSI to lease extra equipment and to spend more time dredging the area, and as a result, it was required to cancel a subsequent dredging contract in Boston, depriving it of additional revenue. Furthermore, a survey of the site commissioned by Atkinson after NDI's demobilization revealed that some of the submerged land, particularly that located in the "expanded" area, was not at the proper elevation.


8
Because of these problems, ISSI sent a default notice to NDI in March 1999, asserting that NDI had failed to perform its contractual obligations to provide "diggable" rock and to lower the submerged rock to the proper elevation. Although it made several payments after NDI's demobilization, ISSI refused to pay the remaining $403,431 due NDI under the initial $1.14 million contract price. ISSI also refused to absorb any of the cost of the "Hughes barge," electing to treat the full cost of approximately $126,707 as a component of the drilling and blasting operations for which NDI bore responsibility. Finally, a dispute between Atkinson and ISSI over the cost of the blasting and drilling performed by NDI in the "expanded" area resulted in NDI not receiving any payments for that work, as the contract provision dealing with work outside the target area stated that NDI would only receive a proportional share of the payments that ISSI obtained from Atkinson and ISSI did not initially seek such sums.


9
On April 29, 1999, NDI sued ISSI in the Superior Court of Sagadahoc County, Maine, claiming breach of contract, unjust enrichment, quantum meruit, and equitable accounting, as well as a cause of action under Maine law for delayed contractor payments, 10 M.R.S.A. § 1114(4). ISSI removed the case to federal district court based on the diversity of the parties and the existence of a controversy in the requisite amount, and on June 4, 1999, it filed an answer and counterclaim, asserting that NDI's failure to produce adequately sized rock and to lower the submerged rock to elevation amounted to negligence and a breach of the parties' contract. Both NDI and ISSI subsequently amended their complaints to add as defendants the parties' respective insurance carriers in an attempt to collect on the payment bonds that had been issued during the BIW Project.


10
Following a protracted discovery period, ISSI moved for partial summary judgment on NDI's unjust enrichment and quantum meruit claims. The district court denied this motion on January 5, 2000. Six days later, ISSI moved to continue the trial indefinitely pending resolution of its ongoing dispute with Atkinson over the adequacy of ISSI's performance under the Atkinson-ISSI agreement. The district court also denied this motion. Finally, two weeks before the scheduled start of the trial and weeks after the joinder deadline laid out in the pretrial schedule had passed, ISSI moved under Fed. R. Civ. P. 19(a) to have Atkinson joined as a necessary party. The joinder motion was considered, and denied, by Magistrate Judge Cohen. At the start of the trial, ISSI filed a motion for reconsideration of the magistrate judge's decision on the joinder issue; the district court heard oral arguments and denied the motion.5


11
The district court conducted a six-day bench trial, primarily consisting of the testimony of officials of the two firms and expert witnesses familiar with the industry practices governing drilling, blasting, and dredging work. At the close of all the evidence, ISSI moved for judgment as a matter of law, asserting that NDI could not prevail on its claims because it had breached its obligations under the agreement to blast according to a 6' x 6' grid and to provide "diggable" rock. The district court denied this motion.


12
On March 31, 2000, the court issued its written findings of fact and conclusions of law. The court first found that NDI's decision to deviate from the 6' x 6' blast grid did not constitute a breach of contract because ISSI, despite its expressions of concern, had acquiesced in the enlarged blast pattern. Moreover, the court concluded that NDI had, in fact, adequately blasted the rock down to the proper elevation; it discounted as inconclusive the post-demobilization survey indicating the insufficient elevation of some spots in the target area, noting the possibility that a neighboring sand dump in the Kennebec River may have caused the problem. With respect to NDI's obligation to provide "diggable" rock, however, the district court found that NDI had not fully performed. On this point, the court, relying on expert testimony adduced at trial, construed the term "diggable" rock as it appeared in the contract to mean a quantity of rock in which no more than ten percent of the sample exceeded one cubic yard in volume. In this case, the court found that 30 percent of the rock that NDI had left behind at the BIW Project site exceeded one cubic yard. As to the "consequence" of NDI's incomplete performance, the court determined that the failure to provide "diggable" rock lowered the value of NDI's services by $175,000.6 The court determined that this $175,000 figure for NDI's failure to fully perform was precisely the same amount that ISSI could prove on its counterclaims for negligence and breach of contract, and that it therefore did not matter whether the $175,000 "credit" to ISSI came in the form of a damage award on its counterclaims or as a reduction in NDI's payment claim. Subtracting that $175,000 figure from the remaining amount ($403,431) that ISSI was withholding from NDI, the court determined that NDI was entitled to receive an additional $228,431 from ISSI for the work it had performed under the contract.


13
The district court also addressed NDI's claim of right to payment for its drilling and blasting in the "expanded" area, for which NDI only was to receive "proportional" compensation from the amount Atkinson paid to ISSI, as well as its claim for a partial credit for the "Hughes barge," a cost that it had been required to fully absorb. The court relied on trial testimony establishing that Atkinson and ISSI were on the verge of concluding a settlement in which Atkinson would pay ISSI $140,000 for drilling and blasting done outside the contract area,7 and concluded that the $140,000 figure was an accurate assessment of the amount that ISSI was entitled to receive from Atkinson. Alternatively, the district court found that NDI was deserving of payment for its work in the expanded area because "ISSI had the obligation to make a reasonably timely request upon Atkinson [for payment] and failed to do so." Northeast Drilling, Inc., 2000 WL 761020, at *2. Going further, the court determined that "[b]ecause ISSI is the only party that knows what NDI's proportional share is and because ISSI has provided no evidence on this topic, there is no basis on which to reduce the $140,000, and I find that NDI is entitled to the full $140,000." Id. As to the "Hughes barge," the court found that under the anticipated Atkinson-ISSI settlement, Atkinson was to reimburse ISSI $81,560 for the barge's cost. Since NDI had paid the full cost of the barge through ISSI's backcharging, and had never been reimbursed by either ISSI or Atkinson, the court awarded NDI the full $81,560 that ISSI was to receive from Atkinson for this expense.


14
Finally, the district court determined that NDI was entitled to interest under Maine law, 10 M.R.S.A. § 1114(4), for the delayed payments by ISSI. The court found that ISSI was obliged to pay interest on $83,431 because, although $403,431 remained to be paid on the original contract price, $175,000 of that sum was being deducted by the court for NDI's incomplete performance and ISSI had yet to receive $145,000 from Atkinson. The court further determined that NDI was entitled to recoup reasonable attorney's fees under Maine law, see 10 M.R.S.A. § 1118(4), in an amount "to be apportioned according to the degree of its success." ISSI seasonably filed its notice of appeal.


15
On appeal, ISSI challenges both the district court's factual and legal determinations. On the facts, ISSI points to three findings made by the district court, mainly involving the parties' performance under the contract, that it alleges were erroneous. It also claims that the district court should have made findings on twelve additional points. On the law, ISSI attacks the district court's refusal to grant its motions to continue the trial and to join Atkinson as a party, its denial of ISSI's motion for judgment as a matter of law, and the permissibility of the court's method of assessing ISSI's damages for NDI's imperfect performance.

II. Factual Findings

16
ISSI claims that the district court made three erroneous factual findings in its written opinion. Moreover, it claims that the court erred by not making twelve additional findings of fact that it claims the overwhelming weight of the evidence at trial would compel. According to ISSI, these alleged factual mistakes, which relate to the parties' performance under the contract, demand correction because they played a pivotal role in the district court's legal analysis and award of damages.


17
Under Fed. R. Civ. P. 52(a), we will not disturb the district court's factual determinations unless they are clearly erroneous. See Vinick v. United States, 205 F.3d 1, 6 (1st Cir. 2000) ("Under [the clearly erroneous] standard, we accept the district court's findings of fact unless we are left with the definite and firm conviction that a mistake has been committed.") (internal quotation marks omitted) (quoting Anderson v. City of Bessemer City, 470 U.S. 564, 573 (1985)).

A.

18
ISSI points to three specific factual findings by the district court that it claims were clearly erroneous. Specifically, ISSI challenges the findings of fact regarding its acquiescence in the enlargement of the blasting-grid pattern, its failure to exercise its right to demand a meeting with NDI to discuss NDI's failure to drill and blast properly, and NDI's success in blasting the target area down to the required elevation. We address each alleged error in turn.


19
First, ISSI vehemently disputes the district court's finding that it acquiesced in NDI's expansion of the 6' x 6' blasting grid specified in the contract.8 It notes that Laurie Mason, the president of ISSI, and Robert Mason, ISSI's manager on the BIW Project, each testified at trial that they repeatedly expressed, through letters and conversations, their dissatisfaction with the grid change to NDI's president, Forrest Bradbury. Both testified, moreover, that Bradbury told them not to worry about the modified plan and assured them that "everything will be okay." ISSI argues that this evidence demonstrates that ISSI never gave the go-ahead to NDI to deviate from the initial blast pattern, or, alternatively, that ISSI's approval of the expanded blast grid was conditioned on NDI's reaching a satisfactory result.


20
Based on evidence in the record tending to cast doubt on ISSI's version of the facts, we find that the district court's determination on this point was not clearly erroneous. For instance, ISSI's Laurie Mason sent a letter to NDI's insurance carrier on January 22, 1999 -- after NDI had informed ISSI of its plan to expand the blasting grid -- in which she described NDI's blasting work to date as "satisfactory." Moreover, in a letter to Atkinson dated February 8, 1999, Laurie Mason spoke approvingly of the expanded blasting pattern that had already been used in drilling and blasting operations by NDI. Perhaps most importantly, the Masons' testimony was contradicted by Bradbury, who stated that Robert Mason, who was present at the BIW Project site virtually every day, had agreed, in spite of his trepidation, to go forward with the enlarged grid "if that's what we had to do." Given the conflicting evidence adduced at trial on this point, we cannot say that the district court committed clear error by finding that ISSI acquiesced in NDI's expansion of the 6' x 6' blasting grid.


21
Second, and closely related to the first issue, ISSI claims that the district court was mistaken when it asserted that there had been no NDI-ISSI meeting to discuss NDI's drilling and blasting performance, even though ISSI had the contractual right to summon NDI to such a meeting if NDI was not fulfilling its obligations. Such a finding, according to ISSI, is "clearly erroneous and misleading to the extent it suggests that ISSI did not promptly exercise its right to request such a meeting."


22
Based on our earlier finding that ISSI acquiesced in NDI's expanded-grid blasting plan, the issue of whether ISSI called a formal meeting to object to NDI's performance loses much of its relevance, at least in the context of this appeal.9 Nonetheless, we find that the district court did not clearly err in finding that there was no meeting between NDI and ISSI that had been requested by ISSI. During the period of the BIW Project, at least one meeting, involving Atkinson, ISSI, and NDI, did occur, but the evidence shows that that meeting was convened by Atkinson. Furthermore, ISSI introduced evidence showing that, on March 7 and 10, 1999, it sent letters to NDI demanding a meeting to discuss the ways in which NDI's drilling and blasting were not conforming to the requirements of the contract (including the enlargement of the blasting grid). These letters were sent, however, more than two months after the drilling and blasting began, and well after NDI had completed the lion's share of its work. Moreover, and more to the point, the fact that ISSI requested such a meeting does not negate the challenged finding that there was no such meeting held pursuant to ISSI's contractual right to request one. There was, in sum, no clear error by the district court on this point.


23
Finally, ISSI takes issue with the district court's finding that NDI's drilling and blasting were generally successful in satisfying the contract's elevation requirements. It alleges weaknesses in the testimony by Atkinson's project engineer, Timothy Daniels, that NDI had sufficiently drilled and blasted, noting that Daniels had written a letter to his supervisor on the eve of NDI's demobilization questioning the adequacy of the drilling and blasting work. Moreover, ISSI notes the December 1999 hydrographic survey which found that certain portions of the area that NDI drilled and blasted were at a higher elevation than that called for in the NDI-ISSI agreement. In this regard, it argues that the district court's statement that "[i]t is impossible . . . to tell whether [the elevation was inadequate at the time of the survey] because of unblasted rock or whether it is a result of sand filling in the area that has migrated from a sand dump in the river," Northeast Drilling, Inc., 2000 WL 761020, at *4 n.5, represents an improper shifting of the burden to ISSI to prove NDI's nonperformance.


24
We do not agree with ISSI's argument that the district court clearly erred by relying on Daniels's testimony in concluding that NDI met its obligation to lower the target area to the required elevation. The fact that Daniels may have expressed uncertainty to his superiors as to the sufficiency of NDI's drilling and blasting does not necessarily negate his testimony at trial that, in the final analysis, NDI's performance in lowering the elevation was adequate. Moreover, the hydrographic survey cited by ISSI, which notes the heightened elevation of some spots in the target area, was conducted nine months after NDI demobilized. Given this time lapse, it was not clearly erroneous for the district court to discount this survey, and to find that NDI had met its burden of proving, primarily through Daniels's testimony, its fulfillment of the contractual obligation to drill and blast down to the proper elevations.


25
In sum, on these three factual issues raised by ISSI, the district court, acting as fact-finder, made its determinations based on its reasonable assessment of the conflicting evidence before it. Thus its findings of fact cannot be deemed clearly erroneous, Anderson, 470 U.S. at 574, and must be affirmed.

B.

26
ISSI further claims that, beyond the three allegedly erroneous findings of fact that the district court did make, the court also erred in declining to make findings of fact on twelve additional matters relating to the parties' performance under the contract.10 In the absence of specific findings by the district court on these matters, ISSI asks us to remand the case for additional factfinding, or to fill the gaps ourselves by making those additional determinations that it claims the great weight of evidence adduced at trial would compel.


27
Standing in the way of this request, however, is ISSI's own failure to file a postjudgment motion, under Fed. R. Civ. P. 52(b), asking the district court to amend its findings of fact to include these twelve points. Rule 52(b), in pertinent part, provides that "[o]n a party's motion filed no later than 10 days after entry of judgment [in a case tried without a jury], the court may amend its findings -- or make additional findings -- and may amend the judgment accordingly." Rule 52(b) represents the principal, and preferred, mechanism for challenging the district court's failure to find facts, as it allows a court that has recently tried the case, rather than an appellate tribunal perusing a cold record, to determine the propriety of considering those additional facts. See Consol. Aluminum Corp. v. Foseco Int'l Ltd., 910 F.2d 804, 814 n.9 (Fed. Cir. 1990) ("Rule 52(b), Fed. R. Civ. P., provides for post-judgment motions for findings not made. Counsel should not simply ignore that rule and head off to the appellate court to seek a remand for the making of those same findings."); cf. United States v. Falu-Gonzalez, 205 F.3d 436, 440 (1st Cir.) ("It is a general principle of appellate jurisprudence that a party desiring more particularized findings at the trial court level must request them from the trial court.") (quoting United States v. Tosca, 18 F.3d 1352, 1355 (6th Cir. 1994)), cert. denied, 120 S. Ct. 2731 (2000). When a party complains of incomplete findings of fact after neglecting to file a Rule 52(b) motion, remand is appropriate only in cases where (1) the district court failed to make findings as to a certain fact and (2) that fact is essential to the resolution of a material issue. Glaverbel Societe Anonyme v. Northlake Mktg. & Supply, Inc., 45 F.3d 1550, 1555 (Fed. Cir. 1995).


28
After reviewing the record, we conclude that, even if true, the twelve facts that ISSI seeks to have included as formal findings would be largely redundant or irrelevant, and that appellate factfinding or a remand for additional factfinding by the district court therefore would be inappropriate. We find the proposed findings concerning the timing of NDI's performance to be immaterial because the district court did not determine that the delay created by the sturgeon excused the imperfections in NDI's performance, as ISSI contends in its reply brief. On the contrary, the court's reduction of NDI's damages by $175,000 reflected its view that NDI had rendered deficient performance under the contract. As to those suggested findings that ISSI had paid only a "proportionate share" of the money it received from Atkinson for "extras," we find that they would not negate the court's determination that NDI was entitled to all of the $140,000 for work completed in the "expanded" area. The fact that ISSI had paid a "proportionate share" on other occasions did not eliminate its obligation to prove to the district court what that term meant. Finally, we find that as to the facts relating to the consequences of the deviation from the 6' x 6' blasting pattern, the additional findings proposed by ISSI are irrelevant because the district court found, in a manner that was not clearly erroneous, see Part II.A, supra, that ISSI acquiesced in this modification of the blasting pattern.


29
Accordingly, we decline ISSI's invitation to make findings of fact on the twelve points or to remand the case to the district court for the purpose of requiring it to make such findings.

III. Continuance and Joinder

30
ISSI contends that the district court committed legal error by denying its pretrial motions to continue the trial and to join Atkinson as a necessary party. Both motions constituted an attempt by ISSI to prevent the present case from being decided without reference to ISSI's separate dispute with Atkinson arising out of the BIW Project. We consider each issue separately.


31
A district court's decision to grant or deny a continuance is analyzed under the abuse-of-discretion standard. Amarin Plastics, Inc. v. Md. Cup Corp., 946 F.2d 147, 151 (1st Cir. 1991). Only an "unreasoning and arbitrary insistence upon expeditiousness in the face of a justifiable request for delay will abuse [that discretion]." Id. (quoting United States v. Torres, 793 F.2d 436, 440 (1st Cir. 1986)). Our review of the record convinces us that the district court did not abuse its discretion by declining to grant the continuance. While it might have been helpful to ISSI to have its disagreement with Atkinson resolved before going to trial with NDI, in that it would have fixed the amount it was to receive from Atkinson, virtually all of the issues posed by the present litigation could be determined wholly without implicating the ISSI-Atkinson dispute. We further note that even though ISSI's dispute with Atkinson had not yet crystallized into formal legal proceedings at the time of the continuance request, ISSI nonetheless requested that the trial date in this case be postponed indefinitely. Cf. United States v. Gantt, 140 F.3d 249, 256 (D.C. Cir. 1998) (noting that district court may consider length of delay in deciding whether to grant or deny continuance motion). Given the potentially lengthy delay that this continuance could have caused, and the rather marginal benefit that would have redounded in return, we believe that the district court was well within its discretion in denying the motion.


32
ISSI also attacks the district court's denial of its motion to join Atkinson as a necessary party under Fed. R. Civ. P. 19(a). Consistent with its arguments regarding the continuance motion, ISSI asserts that the commonality of facts between the NDI-ISSI litigation and the ISSI-Atkinson dispute counseled in favor of joining Atkinson as a party in the present lawsuit. ISSI further argues that the district court applied the wrong legal standard in assessing its Rule 19(a) motion.


33
We have recently declined on two separate occasions to decide whether a Rule 19(a) denial should be reviewed de novo or for abuse of discretion because we found in both cases that the distinction would not be outcome-determinative. United States v. San Juan Bay Marina, 239 F.3d 400, 403 (1st Cir. 2001); Tell v. Trustees of Dartmouth Coll., 145 F.3d 417, 418-19 (1st Cir. 1998) (noting in dicta that the panel would be "inclined" to apply abuse-of-discretion standard if it mattered to the outcome). As in those cases, we need not resolve the issue here because doing so would not affect the result.


34
In this case, ISSI moved to join Atkinson as a necessary party well after the passage of the deadline to join additional parties specified in the pretrial scheduling order. It did not ask the court for leave to modify the scheduling order in its Rule 19(a) motion, nor did it articulate subsequently any "good cause" to excuse the belated filing, although it was required to do both in order to move to join a necessary party beyond the specified deadline.11 See Fed. R. Civ. P. 16(b); cf. Hernandez-Loring v. Universidad Metropolitana, 233 F.3d 49, 51 (1st Cir. 2000). ISSI's appellate briefs also fail to explicate its failure to properly raise the issue. In denying ISSI's motion for reconsideration of its decision not to join Atkinson, the district court noted that the failure to meet this deadline constituted an independent ground for denying the motion. We certainly believe that the district court had the discretion to remain faithful to the pretrial scheduling order that it had previously entered. Nickerson v. G.D. Searle & Co., 900 F.2d 412, 422 (1st Cir. 1990) (holding that district court decision not to deviate from final pretrial order constituted neither manifest injustice nor abuse of discretion requiring court of appeals to intervene). Accordingly, we affirm its denial of ISSI's motion to join Atkinson as a party.12


35
IV. "Judgment as a Matter of Law"


36
ISSI's next contention is that the district court committed legal error by denying both its motion for judgment as a matter of law at the close of NDI's evidence and its renewed motion at the close of all the evidence. It claims that NDI breached the parties' contract by deviating from the 6' x 6' blasting pattern and by failing to produce "diggable" rock. Given these breaches, ISSI insists, NDI was precluded from prevailing on its contract claims as a matter of law.


37
In their briefs, both parties have erroneously characterized ISSI's motions for judgment as a matter of law as arising under Fed. R. Civ. P. 50. Because the trial was heard without a jury, ISSI's motion at the close of NDI's case should have been characterized as a motion for judgment on partial findings under Fed. R. Civ. P 52(c). Rego v. ARC Water Treatment Co.., 181 F.3d 396, 401 (3d Cir. 1999) ("Rule 50(a) applies in jury trials and Rule 52(c) applies in non-jury trials."). Moreover, because ISSI put on evidence following the district court's denial of the motion for judgment on partial findings, it waived its right to appeal from the denial of that motion. N.Y. State Elec. & Gas Corp. v. Sec'y of Labor, 88 F.3d 98, 108 (2d Cir. 1996) (citing Bituminous Constr., Inc. v. Rucker Enters., Inc., 816 F.2d 965, 967 (4th Cir. 1987)). Consequently, we treat the arguments ISSI makes on appeal under the heading of "motion for judgment as a matter of law" simply as challenges to the factual and legal sufficiency of the district court's determinations based on all the evidence. Seeid. (noting that following denial of Rule 52(c) motion the sufficiency of the evidence is analyzed on appeal by viewing the entire record). Following a completed bench trial, of course, we review the court's factual determinations for clear error and its legal conclusions de novo. Commercial Union Ins. Co. v. Seven Provinces Ins. Co., 217 F.3d 33, 40 (1st Cir. 2000), cert.denied, 121 S. Ct. 1084 (2001).


38
On the portion of ISSI's argument that relates to NDI's deviation from the initial blasting scheme, we have little trouble affirming the district court's conclusion. Given the district court's factual finding that ISSI acquiesced in the enlargement of the 6' x 6' grid (and our determination that that finding was not clearly erroneous), it cannot be said that the deviation prevented NDI from prevailing, as a matter of law, on its contract claims.13 By acquiescing in the modified blasting pattern, ISSI effectively relinquished its right under the contract to have blasting performed according to the 6' x 6' grid.


39
The second part of the argument concerns the district court's allegedly erroneous interpretation of the term "diggable" in the contract. The district court, relying on trial testimony as to the meaning of "diggable" in the absence of an explicit contractual definition, construed the term to mean a quantity of rock in which no more than ten percent may exceed one cubic yard. The court further found that 30 percent of the rock at the BIW Project site had a volume of more than one cubic yard, and that the value of NDI's performance to ISSI had been diminished by $175,000 due to this failure to perform fully. ISSI argues that the contract did not provide for this ten percent "error rate," and that the district court committed "clear error of law [in] rewrit[ing] the contract" to allow for the ten percent deviation. It further argues in its opening brief (although it does not make the point with great clarity) that NDI's production of a quantity of rock with an oversize rate of either twenty or thirty percent (depending on whose interpretation of the contract is accepted) amounted to a breach of the contract as a matter of law.


40
We first find that the district court did not err in finding that the term "diggable" in the contract allowed for a ten percent oversize rate. Relying on extrinsic evidence in the form of expert testimony, the court determined that this ten percent tolerance threshold represented the industry standard for such drilling and blasting operations, and that the NDI-ISSI contract had incorporated this standard. This was an appropriate method of construing the contract given the ambiguity of the term "diggable."14 Hilltop Cmty. Sports Ctr. v. Hoffman, 755 A.2d 1058, 1063 (Me. 2000); cf. Commercial Union Ins. Co., 217 F.3d at 38-39 (finding that district court properly considered expert testimony on trade usage and industry practice in order to ascertain meaning of ambiguous contract term).


41
Beyond the issue of interpreting the term "diggable," ISSI makes the argument that NDI's failure to produce a quantity of rock meeting that definition amounted to a breach of the contract as a matter of law. The district court, finding the amount by which NDI's defective production of "diggable" rock lowered its performance value to be identical to the amount that ISSI could prove on its breach-of-contract counterclaims (i.e., $175,000), deemed the distinction between substantial performance and partial performance academic in this case. Accordingly, it declined to characterize NDI's performance as either substantial or partial. Northeast Drilling, Inc., 2000 WL 761020, at *7. ISSI insists, however, that under Maine law ISSI was entitled to an explicit determination that NDI had breached the parties' contract, thereby shifting the burden to NDI to establish the value of its deficient performance under the theory of quantum meruit. See Loyal Erectors, Inc. v. Hamilton & Son, Inc., 312 A.2d 748, 756 (Me. 1973) (explicating the elements of quantum meruit under Maine law).


42
We find ISSI's argument on this point to be unavailing. The district court expressly found that no matter who bore the burden of proving the "cost" of NDI's less-than-flawless performance, the result would have been the same: a $175,000 reduction in the amount that NDI would have otherwise received. Regardless of how useful a finding that NDI had breached its contractual duties would have been to ISSI in its dispute with Atkinson (and we doubt it would have been exceedingly so, given the fact that ISSI at all times bore ultimate responsibility to Atkinson for the quality of the end product), we do not agree that ISSI was entitled to have the district court expressly characterize its damages determination as being based on substantial or partial performance.15 Given that the criteria for both theories of damages were found to be fulfilled,16 and given the district court's finding that application of either of the two theories would have produced an identical measure of damages for NDI, we think that the district court could fairly characterize the quantum of damages as being derived alternately from either one. Cf. Northern Heel Corp. v. Compo Indus., Inc., 851 F.2d 456, 473 (1st Cir. 1988) (noting that there is often more than one sufficient method of measuring damages in any given case). We therefore uphold its damages methodology.

V. NDI's Work in the "Expanded" Area

43
ISSI next challenges the district court's findings regarding NDI's work in the "expanded" area. The court found that, pursuant to an anticipated agreement between ISSI and Atkinson, ISSI was about to receive $140,000 for the drilling and blasting work done by NDI outside of the contract area -- a sum that, according to the district court, reasonably represented the value of the work performed by NDI in the "expanded" area. Alternatively, the court found that ISSI could not complain about the fact that it would have to compensate NDI before receiving payment from Atkinson because ISSI had been six months late in requesting such payments from Atkinson. The court also determined that ISSI had failed to meet its burden to establish the "proportional" share of the Atkinson payments that NDI was entitled to receive under the parties' agreement, and accordingly awarded the entire $140,000 sum to NDI. On appeal, ISSI argues that the district court should not have based its award on the uncertain occurrence of the ISSI-Atkinson settlement agreement, nor should it have found that the entire amount of the Atkinson payments belonged to NDI. In the same vein, it contends that the district court should not have credited NDI $81,560 for the "Hughes barge," another expense for which ISSI was expected to receive compensation from Atkinson in the same settlement agreement.


44
At the heart of the first component of ISSI's argument - that the district court erred by finding that Atkinson was about to pay ISSI $140,000 for work in the expanded area -- is the contractual provision stating that NDI would be paid for such work "if and only if ISSI receives compensation." ISSI asserts that under this clause in the contract, Atkinson's remission of fees was a condition precedent to it making any flow-through payments to NDI, and that it was therefore improper for the district court to award anything for work in the expanded area given the absence of a finding that the condition had been met. Although Atkinson and ISSI did reach a settlement covering work in the "expanded" area on or about February 28, 2000, the terms of that settlement have not been divulged. Under these circumstances, it would be improper for us to assume that the expected amount of the settlement agreement was the amount that ISSI actually received. Cf. Mulero-Rodriguez v. Ponte, Inc., 98 F.3d 670, 672 (1st Cir. 1996) (noting that appellate court may only make inferences that can be "drawn from the evidence without resort to speculation") (citing Frieze v. Boatmen's Bank of Belton, 950 F.2d 538, 541 (8th Cir. 1991)).


45
The district court's $140,000 award rested, however, on an alternate ground: that ISSI effectively surrendered its authority to enforce the condition precedent (Atkinson's payment) by waiting six months after NDI's demobilization to submit the change-order requests to Atkinson for NDI's work in the "expanded" area. Under the so-called prevention doctrine, a contractual condition precedent is deemed excused when a promisor hinders or precludes fulfillment of a condition and that hindrance or preclusion contributes materially to the nonoccurrence of the condition. Restatement (Second) of Contracts § 245 (1981). In this case, the court found that in spite of having the information needed to submit change-order requests to Atkinson, ISSI failed to submit such requests until September 1999, or nearly six months after the completion of NDI's work.17 Because this delay materially contributed to Atkinson's failure to pay ISSI before the NDI-ISSI trial, ISSI is estopped from arguing that it was entitled to be paid by Atkinson before it reimbursed NDI for drilling and blasting in the "expanded" area. 13 Richard A. Lord, Williston on Contracts § 39:4 (4th ed. 2000) ("[W]here one improperly prevents the performance or the happening of a condition of his or her own promissory duty, the offending party thereby eliminates it as a condition . . . ."); cf. Moore Bros. Co. v. Brown & Root, Inc., 207 F.3d 717, 724-26 (4th Cir. 2000) (applying prevention doctrine to render inoperative "pay when paid" condition precedent in construction subcontract). Based on this principle, the district court reasonably concluded that the value of the work performed in the "expanded" area was $140,000.


46
Apart from the issue of whether NDI deserves any payments given the uncertainty surrounding the payments by Atkinson, ISSI further contends that the district court committed error by awarding all of the $140,000 sum to NDI. Under the contract, NDI was to receive a "proportional" share of the amount ISSI received from Atkinson; this critical term in the contract, however, was unaccompanied by further elaboration. ISSI claims that the court erred by determining that "[b]ecause ISSI is the only party that knows what NDI's proportional share is and because ISSI has provided no evidence on this topic, there is no basis upon which to reduce the $140,000 . . . ." Northeast Drilling, Inc., 2000 WL 761020, at *2. ISSI points to the trial testimony of Laurie Mason, who was asked to discuss the manner in which ISSI would tally NDI's "proportional" share. In that testimony, Laurie Mason noted that ISSI would make those payments to NDI according to the same ratio by which it had paid NDI for NDI's drilling and blasting work in the contract area. She neglected, however, to disclose what that ratio was. On appeal, ISSI attempts to make up for this omission by proposing a formula by which this court could ascertain the proper amount. That suggested formula, however, was not presented to the district court; and absent extraordinary circumstances not present in this case, we may not entertain newly proffered evidence for the first time on appeal. In re Colonial Mortgage Bankers Corp., 186 F.3d 46, 50 (1st Cir. 1999), cert. denied, 528 U.S. 1139 (2000). As the district court noted, because the proportion of the Atkinson payments that would pass to NDI was a fact about which ISSI had exclusive knowledge (as NDI apparently had no control over the size of its "proportional" share for work in the expanded area), ISSI's failure to divulge that fact meant that NDI was entitled to all of the payments. Cf. United States v. N.Y., New Haven & Hartford R.R. Co., 355 U.S. 253, 256 n.5 (1957) ("The ordinary rule, based on considerations of fairness, does not place the burden upon a litigant of establishing facts peculiarly within the knowledge of his adversary."); Selma, Rome & Dalton R.R. v. United States, 139 U.S. 560, 567-68 (1891) (holding that burden of proof regarding right to payment rests with party possessing relevant account books).


47
ISSI also attacks the district court's award of $81,560 to NDI for the cost of the "Hughes barge." The court's award was based on ISSI's backcharging of NDI for the cost of this additional equipment, which NDI needed to procure to make up for the time it had lost in its drilling and blasting operations. The district court found that as part of the pending settlement agreement in which Atkinson would agree to pay ISSI for the work in the "expanded" area, Atkinson also would pay ISSI $81,650 to partially defray the cost of the "Hughes barge." Since ISSI never absorbed any expense for this barge, the court found, that payment should completely pass through to NDI. In light of our finding that ISSI is estopped from asserting the condition precedent of Atkinson's payment for extras, we find no reason to set aside the reasonable determination by the district court that NDI is entitled to partial reimbursement for the cost of this additional expense.18


48
Finally, ISSI attempts to impugn the district court's award of interest under the prompt-payment statute, 10 M.R.S.A. § 1114(4). Its argument on this point, however, is neither well developed nor supported by case law, and consequently has been waived. United States v. Zannino, 895 F.2d 1, 17 (1st Cir. 1990).

Conclusion

49
This is a classic construction case, with both parties attempting to advance their respective versions of the facts by adverting to the plethora of letters that they prepared over the course of the BIW Project with an eye toward litigation. As is often the case with disputes of this ilk, the district court found that the substance of those letters generally did not mesh with the reality of the interactions between NDI and ISSI, and that the true nature of the parties' relationship could most accurately be divined by weighing the credibility of those testifying at trial. Our careful review of the record reveals no basis for disturbing those findings of fact reached by the district court in this fashion. Nor do we find any reversible error in the court's legal conclusions. The judgment of the district court is therefore


50
Affirmed. Costs to appellees.



Notes:


*
 Of the District of Rhode Island, sitting by designation


1
 This amount later grew to $1,182,561.16 based on additional work that NDI completed pursuant to approved "change orders" submitted to ISSI during the course of the Project.


2
 According to the initial 6' x 6' grid scheme, NDI would drill a row of holes six feet apart in the rock, then drill another row six feet away from the first row. NDI would then insert blast charges in the holes and then simultaneously detonate several rows of charges.


3
 Under the Atkinson-ISSI contract, ISSI was to seek payment for work in this "expanded" area by submitting change-order requests to Atkinson before authorizing NDI to begin drilling and blasting work.


4
 Before demobilizing, NDI used a jackhammer on the oversize rocks in an attempt to reduce their size. However, NDI was not able to remedy the problem to ISSI's satisfaction using this approach.


5
 In its later written opinion, the district court reaffirmed this finding, stating that "NDI's lawsuit is not to be dismissed for insufficient joinder in failing to make Atkinson a party. (ISSI was free to make Atkinson a party if it chose to do so.)". Northeast Drilling, Inc., 2000 WL 761020, at *8.


6
 As to how it arrived at the $175,000 figure, the court stated that it represented neither a "precise number that can be calculated arithmetically from specific exhibits" nor an "average [or] attempt to 'split the difference,'" but rather a "factfinder's conclusion of what the approximately correct number is when the parties have presented damage numbers at the polar extremes in a factual setting of great uncertainty and difficulties of proof (i.e., what happened underwater and why)." Northeast Drilling, Inc., 2000 WL 761020, at *7.


7
 Although the district court stated in its March 31, 2000 opinion that a settlement agreement between Atkinson and ISSI was pending, that agreement apparently had been reached on February 28, 2000, between the end of the trial in this case and the issuance of the court's opinion. While the occurrence of this agreement has been made part of the record in this case, its terms have not.


8
 The Supreme Judicial Court of Maine has held that the issue of whether a party has relinquished a contractual right is typically a question of fact. Colbath v. H.B. Stebbins Lumber Co., 144 A. 1, 4 (Me. 1929).


9
 At oral argument, counsel for ISSI noted that ISSI is currently in litigation with Atkinson over the issue of whether ISSI upheld its obligations under the terms of the February 2000 settlement agreement. In this context ISSI, in characterizing its response to NDI's drilling and blasting operations, understandably seeks to avoid putting itself, metaphorically speaking, between a rock and a hard place: if it fails to argue in the present case that it did everything it could to ensure NDI's adequate drilling and blasting, it risks undermining its argument in the Atkinson litigation that it properly supervised the drilling and blasting work by NDI for which it shouldered ultimate responsibility under the Atkinson-ISSI contract.


10
 Specifically, ISSI claims the district court should have made findings as to the following points: (1) the original blast schedule that ISSI provided to Atkinson regarding cells 8, 9, and 10 of the blasting map provided for a test blast on November 24, 1998, and additional blasting and shooting from November 26, 1998, to January 15, 1999; (2) the parties were on standby on November 24, 1998, because of the sturgeon's failure to vacate the blasting area; (3) Bradbury did no drilling and blasting during the period of delay; (4) Bradbury got the go-ahead to begin blasting on January 7, 1999; (5) NDI and ISSI amended their contract to delete cells 8, 9, and 10 on December 30, 1998; (6) NDI was ultimately paid by ISSI for some "extras"; (7) when NDI was paid for these "extras," it occurred after ISSI submitted payment for such extras to Atkinson; (8) when ISSI was paid by Atkinson, it paid NDI its "proportionate" share of the extras; (9) Bradbury initially began blasting according to the 6' x 6' grid; (10) according to Mason's testimony, when the 6' x 6' grid was used, there was no problem with producing "diggable" rock; (11) according to testimony of both sides' expert witnesses, blasting pursuant to a 6' x 6' grid using 3.5" holes would produce football-sized rock; and (12) ISSI's expert testified that, based on past work on similar jobs, it should have been possible to produce rock that was one foot in size with very little oversize on the BIW Project.


11
 Counsel for ISSI did argue in its motion for reconsideration that the dispute between Atkinson and ISSI essentially did not materialize until after the joinder deadline had passed in the present suit. This observation, however, overlooks the fact that even if NDI's drilling and blasting were inadequate, a fact that ISSI could have ascertained at the time of NDI's demobilization, it did not relieve ISSI's obligation to Atkinson to dredge to the proper elevation. In other words, while the sufficiency vel non of ISSI's dredging was at the core of the Atkinson-ISSI dispute, the adequacy vel non of NDI's drilling and blasting under the NDI-ISSI agreement was not.


12
 In so ruling, we expressly decline to consider the district court's alternate ground for denying ISSI's joinder motion, namely, that Atkinson was not a "necessary" party within the meaning of Rule 19(a).


13
 In its argument on this point, ISSI attacks a remark by the district court that "NDI did breach the contract [by] . . . fail[ing] to amend the blast plan or [to] follow it precisely -- but none of these breaches was material or caused ISSI any quantifiable damage." Northeast Drilling, Inc., 2000 WL 761020, at *4. The nonmaterial "breach[es]" to which the district court refers in this statement appear to be the failure to adjust the blast plan document and the failure to conform precisely to the modified understanding between the parties -- not the earlier decision to abandon the original 6' x 6' blasting plan.


14
 Under Maine law a contract term is deemed ambiguous when it is "reasonably susceptible of different interpretations." Guilford Transp. Indus. v. Pub. Utils. Comm'n, 746 A.2d 910, 914 (Me. 2000) (quoting Portland Valve, Inc. v. Rockwood Sys. Corp., 460 A.2d 1383, 1387 (Me. 1983)). Under this standard we agree with the district court's conclusion that the term "diggable" is an ambiguous one, given that there is neither a generally prevailing definition for the term nor clarification as to its meaning elsewhere in the contract. Id. at 914-15.


15
 ISSI relies heavily on our decision in Combustion Engineering, Inc. v. Miller Hydro Group, 13 F.3d 437 (1st Cir. 1993), as support for its argument that NDI breached the contract as a matter of law by producing oversize rock at a 20 percent higher rate than that allowed under the definition of "diggable" rock. Applying Maine law in Combustion Engineering, we found that the district court did not err in finding that the builder of a hydroelectric facility breached the construction contract with its client by erecting a dam that produced a water flow exceeding the contract specifications by 15.38 percent. Id. at 442-43. ISSI points to that finding and asserts that, afortiori, NDI's 20 percent deviation in this case must represent a breach. Nowhere in Combustion Engineering, however, did we hold that there is a certain performance threshold below which a court must find breach of contract as a matter of law.


16
 Specifically, the district court found that NDI had acted in good faith in its work under the contract, had significantly performed to that end, and had conferred a material benefit upon ISSI. By establishing these elements, NDI validly asserted a claim of quantum meruit under Maine law, thereby entitling it to the value of the work it did perform. Loyal Erectors, Inc., 312 A.2d at 756. Alternatively, if NDI substantially performed under the contract, it was entitled to receive the contract price less damages on account of the omissions. F.A. Gray, Inc. v. Weiss, 519 A.2d 716, 717 (Me. 1986).


17
 ISSI disputes the district court's factual finding that ISSI was responsible for the delayed change-order request. It claims that NDI, by refusing to respond to ISSI's requests for backup information, prevented ISSI from completing the necessary paperwork. Even if NDI did fail to respond to ISSI's requests for supplemental information, however, that fact does not contradict the district court's finding that at the time of NDI's demobilization, ISSI had all the information it needed to submit an adequate change-order request.


18
 ISSI also challenges the district court's finding that NDI had not agreed to absorb the full cost of the barge under the extant circumstances. After reviewing the conflicting evidence in the record on this point, we conclude that the court's determination was not clearly erroneous.


