TORRUELLA, Chief Judge.

Plaintiff, Teamsters Local 379 (“Teamsters” or the “Union”), filed grievances against eight Boston Harbor Project einploy-ers .on behalf of certain truck drivers on the project who own and drive their own trucks (the “owner-operators”) and are engaged in the transportation and removal of fill from the construction site. The Teamsters argued that those drivers were entitled to receive the various fringe benefit payments received by project employees. The subject of the present dispute is whether the owner-operators qualify as “independent contractors” or as “employees” under the Labor Management Relations Act (LMRA), 29 U.S.C. §§ 141, et seq. The arbitrator assigned to this case concluded that the owner-operators are “employees,” and thus entitled to receive the benefit payments. The district court reversed this finding, ruling that the owner-operators are “independent contractors,” and that any payment of benefits would violate section 302 of the LMRA, 29 U.S.C. § 186. After careful review, we affirm the district court.

BACKGROUND

Underlying the grievances in this case is the Harbor Project Labor Agreement (the '“Project Agreement”), entered into by the Union and various contractors (or “project managers”) engaged in the construction of waste water treatment facilities on Deer Island in the Boston Harbor (the “Boston Harbor Project”). After years of using private owner-operators for hauling their construction materials, wastes, and fills on the construction site without making any fringe benefit contributions on their behalf, project managers received complaints from the Union on March 2, 1992, for allegedly violating the Project Agreement. In 1994, this court decided Labor Relations Div. of Constr. Industries of Mass. v. Teamsters Local 379, 29 F.3d 742 (1st Cir.1994) (“Teamsters /”), which stemmed from those grievances. In Teamsters I, we affirmed an arbitrator’s finding that the Project Agreement must be read to incorporate certain provisions of the earlier Massachusetts Teamsters’ Heavy Construction Agreement (“Teamsters’ Agreement”) which obligates employers to make health insurance and pension contributions on behalf of the owner-operators. •

However, we remanded the case to the arbitrator to determine whether the owner-operators would be considered “independent contractors” or “employees” under the LMRA. If the owner-operators fall into the “independent contractors” category, certain fringe benefit payments on their behalf would violate the LMRA, 29 U.S.C. § 186, which prohibits such payments to labor unions unless the payments are made to trust funds “for the sole and exclusive benefit of the employees of such employer.” 29 U.S.C. § 186(c)(5) (emphasis added). Thus, unless the owner-operators are considered “employees,” the Project Agreement is unenforceable insofar as it requires illegal benefit payments to be made to a labor union. If the project managers were to make contributions for the benefit of independent contractors, they, and the Union, could be subject to federal criminal prosecution.

On remand, the arbitrator assigned to the case concluded that the owner-operators are employees, and not independent contractors. After a thorough review of case law and agency doctrine, the arbitrator applied'a mul-ti-factored test which incorporated common law agency principles and a so-called “economic realities” test (which focused on the financial independence of the workers) in order to determine that the truck owner-operators are significantly similar to other employees on the Boston Harbor Project. This finding was appealed to the district court.

*16 Because an interpretation of a federal criminal statute was involved, the magistrate and district court thoroughly reviewed the arbitrator’s findings. See Teamsters I, 29 F.3d at 747-48; Washington Post v. Washington-Baltimore Newspaper Guild, Local 35, 787 F.2d 604, 606 (D.C.Cir.1986). Ultimately, the district court, adopting a lengthy and equally thorough report and recommendation from the magistrate, reversed the arbitrator. The magistrate reported that the arbitrator had seen fit to “disregard uncon-tradicted evidence and controlling principles of law to reach a result that accorded with his own notions of industrial justice.” Now, once again, this case has been appealed to our court.

ANALYSIS

I. Preliminary Arguments

Before we proceed, we must address two separate arguments put forward by the Union as to why this proceeding is unnecessary. According to both of these arguments, the project managers are required to make the benefit payments at issue even if an application of the common law of agency .shows that the owner-operators are independent contractors. Neither argument has merit.

The Union’s first argument is premised upon LMRA section 302(c)(2), which explicitly exempts any payments made in satisfaction of an arbitrator’s award from section 302(a)’s general prohibition on employers’ payments to labor organizations. See 29 U.S.C. § 186(a) & (c)(2). The union claims that the employers in this case would, therefore, not be subject to prosecution under the LMRA since any payments that the project managers would make on behalf of the owner-operators would be made pursuant to the arbitrator’s interpretation of the Project Agreement. The Union believes that the concern we expressed in Teamsters I that enforcement of the Project Agreement could subject the employers to federal prosecution, see 29 F.3d at 748, was unwarranted and our remand unnecessary.

The Union, however, fails to take into account the entire text of LMRA section 302(c)(2), which exempts employers’ payments to labor organizations from section 302(a) only where those payments are made in satisfaction of an arbitrator’s award “in compromise, adjustment, settlement, or release of any claim, complaint, grievance, or dispute....” 29 U.S.C. § 186(c)(2). The arbitrator’s decision affirmed in Teamsters I interpreted the Project Agreement as requiring, by its own terms, that project managers make benefit payments on behalf of the owner-operators. Thus, project managers were required by their contract to make the benefit payments on behalf of the owner-operators before the arbitrator ever read the Project Agreement, and are not required to make payments in satisfaction of any settlement, or for release of any claim. LMRA section 302(c)(2) is therefore irrelevant.

Under the Union’s flawed interpretation of the LMRA, any employer and union wishing to circumvent section 302’s prohibition on direct payments to labor organizations could simply contract to do so in plain terms, and then engage an arbitrator to interpret that contract. We decline to read such an enormous loophole into the statute against its plain language.

The Union’s other argument that purportedly moots this appeal is no more useful. According to the Teamsters, the employers may be obligated to contribute to benefit funds for hours worked by subcontractors even when those same subcontractors are legally ineligible to receive those funds, which are “for the sole and exclusive benefit of the employees-” 29 U.S.C. § 186(c)(5). This argument follows from the Supreme Court’s logic in Walsh v. Schlecht, 429 U.S. 401, 407-410, 97 S.Ct. 679, 50 L.Ed.2d 641 (1977), which held that if an employer is contractually bound to make trust fund contributions based on the hours worked at a job site by individuals other than its own employees, then, so long as the individuals cannot enjoy those benefits, the employer does not violate section 302 of the LMRA when it performs its obligation. See also Illinois Conference of Teamsters and Employers Welfare Fund v. Mrowicki, 44 F.3d 451, 461 (7th Cir.1994) (extending Walsh to health and welfare benefit contributions). Those funds would then be held in trust by the Union. The Team *17 sters note that the Project Agreement only requires contributions for owner-operators based upon their hours worked, and argues that the grievance underlying this case was primarily concerned with whether the project managers were required to make the contributions, not whether owner-operators were eligible to receive benefits. Thus, according to the Union, this case is governed by Walsh and Mrowicki, and our remand in Teamsters I was unnecessary.

Unfortunately for the Union, this argument comes too late. In Teamsters I, we noted that “[njeither party disputes that the plaintiffs’ payment of fringe benefits on behalf of the owner-operators [would be] illegal under Section 302 if the owner-operators are independent contractors rather than employees.” Id. at 748. We based this conclusion on the Union’s previous filings, wherein the Teamsters had demanded “that all Health and Welfare contributions and all Pension contributions be made on behalf of all truck drivers” while acknowledging that it did “not dispute the proposition that Section 302 prohibits fringe benefit contributions on behalf of independent contractors.” The Union claimed that its grievance was filed on behalf of “certain truck drivers who were not receiving fringe benefits” even though “the owner-operators were entitled to fringe benefit coverage.” In Teamsters I, the Union presented only one argument on the LMRA section 302 issue in this case, i.e., that the arbitrator correctly, if implicitly, found that the owner-operators were employees. We determined that this argument could only be properly resolved after remand. See 29 F.3d at 748-49.

Tardily, the Union tries to reverse course, after remand, by arguing that it is entitled to trust fund contributions based upon hours worked by owner-operators, even if they are found to be independent contractors ineligible to benefit from those trust funds. The arbitrator, when first presented with this case, could have determined whether the Teamsters Agreement required fringe benefit contributions based upon the hours worked by independent contractors. He did not make such a finding because he was not asked to do so. Had the Union made this argument at any time prior to the remand in Teamsters I, we might have considered asking the arbitrator to address this issue. However, the introduction of the issue at this late date would require another remand, and we are unwilling to further delay this already ancient dispute.

When a party could have raised an argument in his initial appeal, and failed to do so, he has generally waived his right to raise that argument on remand or on appeal from remand. See United States v. Adesida, 129 F.3d 846, 849-50 (6th Cir.1997); Harmon v. Thornburgh, 878 F.2d 484, 496 (D.C.Cir.1989); Omni Outdoor Adver., Inc. v. Columbia Outdoor Adver., Inc., 974 F.2d 502, 506 (4th Cir.1992). This ease is no exception. An examination of the Teamsters’ Agreement reveals that the Union’s interpretation, although not unreasonable, is not “so compelling as to virtually insure appellant’s success.” 1 Credit Francais International, S.A. v. Bio-Vita, Ltd., 78 F.3d 698, 709 (1st Cir.1996) (raise-or-waive rule will only be ignored where the new argument is “so compelling as virtually to insure appellant’s success, and a gross miscarriage of justice would result from the failure to address it.”) (citations omitted). Moreover, Walsh had been decided long before the grievance underlying *18 this case was ever filed, and the Union has failed to provide any explanation of its failure to raise this argument earlier. Cf. Old Ben Coal Co. v. Director, Off. of Workers’ Compensation Programs, U.S. Dept. of Labor, 62 F.3d 1003, 1007 (7th Cir.1995) (presumption of waiver for arguments first raised on remand can be overcome where those arguments- are based upon important intervening case law which could not have been considered during initial appeal). We must deem the argument waived.

II. Standard of Review

In Teamsters I, we held that:

[T]he issue of whether fringe benefit contributions on behalf of the owner-operators is illegal under federal law does not involve the same type of circumscribed judicial review that we afford arbitration decisions grounded in interpretations of a contract. Although the arbitrator’s factual findings regarding the status of the owner-operators under Section 302 of the LMRA/29 U.S.C. § 186, may deserve a certain amount of deference, the issue of illegality is ultimately one for federal court review. Given that a determination under § 302 could have criminal consequences, the plaintiffs deserve a thorough judicial review of an arbitrator’s decision as to this issue.... We are not prepared, however, to conduct that analysis ourselves without first giving the arbitrator the opportunity to reexamine the factual circumstances of this case.... [T]he arbitrator can play an important role in providing first-hand factual findings for the benefit of the reviewing court.

29 F.3d at 747-49 (citations omitted).

Despite this seemingly clear review of the responsibilities of the arbitrator and reviewing district court on remand, the parties, and indeed the arbitrator himself, have since expressed confusion regarding the deference to which the arbitrator was entitled on his determination of the owner-operator status. We thus revisit the issue, with an eye towards further clarifying the' roles that an arbitrator and reviewing court play when applying a statute to a body of facts.

“It is by now a familiar rule that an arbitrator’s award is entitled to significant deference.” Washington Post, 787 F.2d at 606. In fact, where the parties have previously bargained for the benefit of an arbitrator’s expertise in settling any contractual disputes, the courts have “no business weighing the merits of the grievance, considering whether there is equity in a particular claim, or determining whether there is particular language in the written instrument which will support the claim.” United Steelworkers of Am. v. American Mfg. Co., 363 U.S. 564, 567-68, 80 S.Ct. 1343, 4 L.Ed.2d 1403 (1960). Therefore, courts hearing appeals from arbitration awards interpreting contracts must tread much more gingerly than appellate courts reviewing district court decisions. See United Paperworkers Int’l. Union v. Misco, Inc., 484 U.S. 29, 37-38, 108 S.Ct. 364, 98 L.Ed.2d 286 (1987).

“Despite this rule, it is unquestionably the province of the courts to say what the law is. We need not defer to an award which contemplates a violation of law.” Washington Post, 787 F.2d at 606. When an arbitrator’s interpretation of a contract potentially exposes a party to federal prosecution, the courts become more active. The law is our charge, and our responsibility to interpret it cannot be abdicated. Insofar as and only insofar as an arbitrator’s findings and conclusions will determine the reach of a federal criminal statute into a dispute with which he is involved, his findings of fact will be reviewed. for clear error and his legal conclusions de novo. See id.; International Brotherhood of Electrical Workers, Local 97 v. Niagara Mohawk Power Corp., 143 F.3d 704, 726 (2d Cir.1998). This doctrine flows, in part, from the observation that private parties must not be empowered to contract out of a thorough judicial review of their potentially criminal activities. Cf. Misco, 484 U.S. at 42, 108 S.Ct. 364 (observing that “the public’s interests in confining the scope of private agreements to which it is not a party will go unrepresented unless the judiciary takes account of those interests ... ”). The doctrine also reflects the interest of private parties in not being compelled to engage in conduct that might subject them to criminal prosecution. This provides for a limited *19 “public policy” exception to the standard of review normally applied to an arbitrator’s decisions whereby “as long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority, that a court is convinced he committed serious error does not suffice to overturn his decision.” Id. 108 S.Ct. at 371, quoted in S.D. Warren Co. v. United Paper-workers’ Intern’l Union, Local 1069, 845 F.2d 3, 7 (1st Cir.1988).

It was against this backdrop that we declared ourselves “too far removed from the dispute” to make the necessary “first-hand factual findings” necessary to properly resolve this case four years ago. Teamsters I, 29 F.3d at 749. Now, on review, we afford those first-hand factual findings great deference, with far less deference to those findings which are based only upon the arbitrator’s analysis and synthesis of the existing record, and no deference for the arbitrator’s purely legal application of federal law to those facts. Again, let us be clear about the unusual circumstances of this case which empower us to review this arbitrator’s findings so thoroughly. We are not determining anyone’s rights under contract in this appeal, but instead whether adherence to the Project Agreement, as interpreted by the arbitrator, requires criminal conduct. Under these circumstances, we would be derelict in our duties if we were to afford the arbitrator greater deference than this.

The arbitrator’s decision reveals that he took the time and effort required to thoroughly review caselaw and to assemble a detailed list of relevant factors to consider in determining whether the owner-operators are employees or independent contractors. The decision also reveals that the arbitrator relied very little upon his first-hand observations in making his decision. As the magistrate judge observed, despite the fact that the arbitrator visited the construction site in 1995, he makes no explicit reference to his personal observations in his 28-page decision. While we acknowledge that the fact-finder’s personal observations may have implicitly influenced certain factual conclusions, reading the arbitrator’s decision informs us that the bulk of his findings were premised solely upon his synthesis and analysis of the record in comparison with other relevant Circuit and Supreme Court cases. Thus, most of the arbitrator’s opinion stems from an interpretation of the common law, which, though carefully constructed and somewhat helpful, is not entitled to much deference from this court under the circumstances of this case.

III. Common Law Agency Analysis

In order to determine whether the owner-operators are employees of the project managers under the LMRA, we must look to general principles of the common law of agency. See Teamsters I, 29 F.3d at 748. Applying the common law to determine whether owner-operator truck drivers are employees or independent contractors is nothing new to this or other federal appellate courts. See United States v. Silk, 331 U.S. 704, 67 S.Ct. 1463, 91 L.Ed. 1757 (1947); NLRB v. Amber Delivery Service, Inc., 651 F.2d 57, 63-64 (1st Cir.1981); Berger Transfer & Storage v. Central States, Southeast and Southwest Areas Pension Fund, 85 F.3d 1374, 1379 (8th Cir.1996); C.C. Eastern, Inc. v. NLRB, 60 F.3d 855, 860-61 (D.C.Cir.1995); North American Van Lines, Inc. v. NLRB, 869 F.2d 596, 604 (D.C.Cir.1989); NLRB v. A. Duie Pyle, Inc., 606 F.2d 379, 387-88 (3d Cir.1979); Merchants Home Delivery Service, Inc. v. NLRB, 580 F.2d 966, 975-76 (9th Cir.1978); Associated Gen. Contractors of Cal., Inc. v. NLRB, 564 F.2d 271, 280 (9th Cir.1977). In doing so, the fundamental inquiry is whether the employer has the “right to control the manner and means by which the product is accomplished.” Nationwide Mut. Ins. Co. v. Darden, 503 U.S. 318, 323, 112 S.Ct. 1344, 117 L.Ed.2d 581 (1992). This is the so-called “right to control” test. In applying this multi-factored test, “all of the incidents of the relationship must be assessed and weighed with no one factor being decisive.” Id. at 324,112 S.Ct. 1344 (quoting NLRB v. United Ins. Co. of Am., 390 U.S. 254, 258, 88 S.Ct. 988, 19 L.Ed.2d 1083 (1968)); Teamsters I, 29 F.3d at 748.

While no one factor is decisive in this determination, there can be little doubt of the prominence of the factor of entrepre *20 neurial risk and reward, i.e., “‘Employees’ work for wages or salary ... [while] ‘Independent Contractors’ ... depend for their income ... upon the difference between what they pay for goods, materials, and labor and what they receive for the end result, that is, ... profits.” H.R.Rep. No. 245, 80th Cong., 1st Sess. 18 (1947), reprinted in 1 Legislative History of the Labor Management Relations Act, 1947, at 309 (1948); see also C.C. Eastern, 60 F.3d at 858-61; A. Duie Pyle, 606 F.2d at 382. This important factor clearly militates in favor of a finding of “independent contractor” status in this case. The owner-operators here bear the costs of owning and insuring their own trucks, and cover fuel, repair, and tax expenses stemming from the operation of those vehicles. Both the arbitrator and the district court acknowledge that this factor favors the position of the project managers.

The arbitrator, however, reasoned that the degree of control that the project managers exercised over the manner in which the owner-operators performed their work was so great as to overcome the entrepreneurial risk and reward factor. It is true that this court has determined that the degree of control exercised over' owner-operators may be so complete as to support a determination that an employer-employee relationship has been created despite the fact that the owner-operators own their own equipment, pay their own expenses, and purchase their own insurance. See Amber Delivery Service, 651 F.2d at 63-64. However, we must agree with the district court’s conclusion that this is not such a case. Upon examination, the arbitrator’s erroneous conclusions can be traced to a misunderstanding of the “right to control” test, unsupported findings of fact, and a failure to appreciate the significance of further key evidence of an independent contractor relationship.

An employer will always control the result to be achieved on a given project, whether an employer-employee or independent contractor relationship exists. The difference in agency status, then, lies in whether the manager controls the means of obtaining that result. See C.C. Eastern, 60 F.3d at 858. With this background, we conclude that the arbitrator erred when he relied upon the fact that the project managers control where, when, and how often loads are necessary for transport in order to support a finding of an employee-employer relationship. Such would be the case regardless of the employment relationship of the drivers and the managers.

Other similar errors appear in the arbitrator’s decision. For example, the arbitrator regarded the following factors as important evidence of an employer-employee relationship: (1) that employers may terminate or shorten the work day due to lack of work; (2) that they require truck loading and off-loading to conform to barge availability; and (3) that the owner-operators have become economically dependent upon the Boston Harbor project. 2 However, these factors do not cut either way. They pertain to the amount and type of work at issue, and not to the degree of control exercised over the means by which that work is accomplished.

When the arbitrator examined relevant factors to the “right to control” test, he reached conclusions which were entirely unsupported by the testimony in this case. For example, he concluded that employers determined the drivers’ routes of travel on Deer Island and subjected owner-operators to constant on-site supervision. The transcript, however, clearly reveals that the Massachusetts Water Resources Authority, a public *21 authority, determined routes of travel, and, furthermore, there was simply no evidence to support the arbitrator’s conclusion that owner-operators were subject to constant supervision.

The arbitrator also failed to recognize the significance of certain evidence supporting independent contractor status. Uncontra-dicted evidence revealed that owner-operators often perform their services for more than one company during the course of a day, sometimes send friends or relatives to drive their trucks in their place, schedule their own rest breaks, and perform their services on whatever days they choose. The arbitrator declined to factor this evidence into his analysis. 3 However, this evidence is highly probative of the agency status in the case, and helps to easily distinguish owner-operators from employees. See Darden, 503 U.S. at 323-24, 112 S.Ct. 1344 (“the extent of the hiring party’s discretion over when and how long to work” and “the hired party’s role in hiring and paying assistants” factor into the common law right of control test); (7.(7. Eastern, 60 F.3d at 860 (whether and how often owner-operators drive for other companies is important to a determination of agency status).

To successfully counter the evidence that the Boston Harbor owner-operators assume entrepreneurial risk and reward while working for numerous different employers each week, the Union would have had to present compelling evidence that owner-operators are subject to a high degree of management control over the means by which they accomplish their job. The Union was clearly unable to meet that burden.

Both parties agree that in NLRB v. Amber Delivery Service, Inc., 651 F.2d 57 (1st Cir.1981), this court set out a proper analysis of agency status disputes involving owner-operator truck drivers. A comparison between the facts of these two cases further illustrates why the Teamsters’ present position is untenable.

In Amber, we expressed doubts about whether the NLRB correctly determined that the owner-operators in that case were employees. See 651 F.2d at 64 n. 8. However, pursuant to the deferential standard of review applicable to that case, we determined that there was insufficient evidence to compel reversal of the Board. Id. Almost none of the factors which made Amber such a close case appear in the present dispute. In Amber, the owner-operator delivery truck drivers were required to report to work by 8:00 a.m. with their vehicles loaded, were required to phone the employer every two hours during the day, were not allowed to reject loads, were prohibited from providing similar services to other employers, were required to attend training and safety meetings and were required to wear company uniforms and paint their vehicles with company colors affix company sign. See id. at 62-63 (explaining that these specific facts were important to the resolution of that case). At the Boston Harbor Project, the owner-operators can begin their work day at any time, occasionally reject loads, provide similar services to other employers, are not required to attend any meetings, and are not required to identify with a given employer by wearing uniforms, painting their trucks or using company signs. Ultimately, despite factors such as the drivers receiving an hourly wage, which would tend to support a finding of an employer-employee relationship, there is insufficient evidence of management control over the manner in which owner-operators work to support the arbitrator’s opinion.

CONCLUSION

For the reasons stated herein, the judgment of the district court is affirmed.

. The Article of the Teamsters' Agreement (as incorporated by the Project Agreement) that deals with benefit contributions reads as follows:

Beginning December, 1, 1990 each Employer agrees to contribute to the Construction Teamsters Health and Welfare Fund the sum of Two Dollars and Sixty-Two Cents ($2.62) per hour for each hour for which an employee receives pay, figured to the nearest quarter hour and an overtime hour shall be considered as a single contribution hour.... If an employee is absent because of illness or off-the-job injury for more than one (1) week and notifies the Employer of such absence, the Employer shall continue to pay the required contributions until such employee returns to work, provided, however, such contributions shall be for thirty-two (32) hours per week and shall not be paid for a period of more than six (6) months.

We are uncertain whether this Article was intended by the contracting parties to require employers to contribute for hours worked by owner-operators who work "on and off” for the employer and who would be legally ineligible to receive benefits by virtue of their “independent contractor” status.

. This arbitrator referred to this final factor, i.e., whether the drivers were economically dependent upon the Boston Harbor Project, as the "economic realities test.” According to the arbitrator, "if the workers ... are economically dependent upon the entity ... from (sic) whom they perform services ... they should be designated as employees.” This "test” is unsupported by law, and strikes the court as incompatible with the interpretation of the LMRA in Nationwide Mut. Ins. Co. v. Darden, 503 U.S. 318, 323, 112 S.Ct. 1344, 117 L.Ed.2d 581 (1992) (applying the multi-factored "right to control” test). Taken to its logical conclusion, this reasoning would convert any situation where a worker performs services for only a single client into an employer-employee relationship, which is obviously not the. law. See Secretary of Labor v. Lauritzen, 835 F.2d 1529, 1541 (7th Cir.1987) (providing, as an example, that “[l]awyers may work for years for a single client but be independent contractors”).

. Curiously, the arbitrator cited to the pages of the transcript containing this evidence as support for his conclusion that the drivers were employees. Thus, if the arbitrator did consider this evidence, he misinterpreted it.