PREGERSON, Circuit Judge:
BACKGROUND
The Railway Labor Act, as amended in 1951, permits employers engaged in interstate rail or air commerce to include in collective bargaining contracts either a union shop or an agency fee provision. Railway Labor Act, § 2, subd. 11, 45 U.S.C. § 152, subd. 11 (hereafter “Section 2, Eleventh”). A union shop provision requires employees to join the union that represents their craft or class. 45 U.S.C. § 152, subd. 11(a). An agency fee provision requires employees to pay the union a fee equal to union dues, initiation fees, and assessments, but does not require employees actually to join the union. 45 U.S.C. § 152, subd. 11(b). Such provisions prevent “free riders” from reaping the benefits of collective bargaining without contributing financial support to the union’s efforts. In Railway Employees’ Department v. Hanson, 351 U.S. 225, 76 S.Ct. 714, 100 L.Ed. 1112 (1956), the Supreme Court upheld the constitutionality of such financial support requirements, specifically rejecting contentions that a union shop provision violated the First and Fifth Amendment rights of protesting employees.
Five years later, in International Association of Machinists v. Street, 367 U.S. 740, 81 S.Ct. 1784, 6 L.Ed.2d 1141 (1961), the Court reaffirmed Hanson, but construed the Railway Labor Act as prohibiting the union from using any portion of an employee’s mandatory dues to support political and ideological causes once the employee has informed the union of his or her objection to those expenditures. That construction allowed the Court to avoid deciding the First Amendment challenge to the use of union dues to support political activities. That issue was not faced until 1977 when, in Abood v. Detroit Board of Education, 431 U.S. 209, 234, 97 S.Ct. 1782, 1799, 52 L.Ed.2d 261 (1977), the Court ruled that the First Amendment prohibits a union from financing political and ideological causes not germane to collective bargaining duties by using a portion of the dues of employees who object to advancing those causes.1
The instant action commenced in 1973, when appellants, a group of Western Airlines employees, challenged the dues payment obligation imposed by a union shop agreement.2 The appellants contended that [1068]*1068they could not be required to contribute to any union costs except those incurred for collective bargaining and grievance administration activities. They urged the district court to define the scope of those activities narrowly. Such a construction would entitle them to a substantial dues rebate.
In October 1975, the union (Brotherhood of Railway, Airline and Steamship Clerks, Freight Handlers, Express and Station Employees, hereafter “BRAC”) instituted a retroactive voluntary rebate program for employees who object to the use of a portion of their dues to support certain political or ideological causes not germane to collective bargaining. BRAC asserts that this rebate plan protects appellants’- rights under Street and Abood with respect to union activities conceded by all to be “political” or “ideological.”
Appellants contend that the plan still violates their First Amendment rights because it provides a rebate rather than an immediate dues reduction, thereby giving the union use of a portion of their dues for up to a full year. They also argue that the union kept inadequate records and could not account accurately for its expenditures.
Appellants next argue that they cannot be charged for certain major operating expenditures of the union. These expenditures were incurred for union activities that include: 1) Grand Lodge conventions; 2) Grand Lodge litigation not having as its subject matter contract negotiation or administration; 3) Grand Lodge publications; 4) Grand Lodge social activities; 5) Grand Lodge death benefits; and 6) Grand Lodge organizing activities. Expenditures for these activities are not “political” or “ideological” and thus not governed by the narrow holdings of Street and Abood. Nonetheless, appellants interpret language in those and other opinions as indicating that such expenditures are not a part of the collective bargaining and grievance administration costs to which objecting employees can be required to contribute. BRAC responds that these activities are sufficiently germane to the collective bargaining process so that all employees under a union shop or agency fee arrangement should be required to shoulder their fair share of the cost of these traditional union activities.
In 1976, the district court granted appellants’ summary judgment motion, holding in paragraph twenty-two of its ruling that the major operating expenditures in question (denominated “Paragraph 22” expenditures or activities) were not incurred for collective bargaining activities. The court thus ruled as a matter of law that protesting employees could not be forced to support the activities listed above through compulsory dues payments. BRAC sought 28 U.S.C. § 1292(b) certification, arguing that the district court’s ruling, which covered the liability issues, extended a dissenter’s entitlement to a rebate beyond the area of political and ideological expenditures. The district court issued the certification but this court declined to hear the matter until after a trial on the damages issues. (BRAC v. Ellis, No. 76-8143, June 7, 1976.)
The district court tried the damages claims in 1978. With respect to certain expenditures, conceded by the union to be political and ideological, the court held that the union’s rebate plan fully protected plaintiffs’ interests. The court then found that approximately forty per cent of the Grand Lodge’s annual expenditures had been for Paragraph 22 activities, i.e., the six activities listed above. The court ruled that these expenditures, as well as minimal Paragraph 22 expenditures made by the Local Lodges and intermediate System Boards, had to be refunded to protesting employees.3
[1069]*1069The protesting employees appealed the decision, contending: (1) that the court erred in declining to adjudicate their First Amendment claims; 2) that the court applied the wrong standard of proof; 3) that the damages award is inadequate because the court did not require the union to account accurately for its expenditures; 4) that the court erred in cutting off plaintiffs’ discovery rights six months before trial; and 5) that the court erred in refusing to consider evidence uncovered by plaintiffs after the trial but before judgment had been rendered.
The union challenged the court’s summary judgment ruling that the six activities enumerated in Paragraph 22 are not germane to collective bargaining.
I. BRAC’S EXISTING POLITICAL-IDEOLOGICAL REBATE PLAN
In BRAC v. Allen, 373 U.S. 113, 83 S.Ct. 1158, 10 L.Ed.2d 235 (1963), the Supreme Court grappled with the problem of providing a practical and adequate remedy to employees who object to a union’s political and ideological expenditures. The Court stated: “The difficulties in judicially administered relief .. . should, we think, encourage petitioner unions to consider the adoption by their membership of some voluntary plan by which dissenters would be afforded an internal union remedy.” Id. at 122, 83 S.Ct. at 1163.
Pursuant to that suggestion, BRAC instituted a voluntary rebate plan in late 1975. Under the program, a protesting employee receives a rebate on his or her pro rata share of all union disbursements for political and ideological activity as well as all legislative and lobbying costs, charitable donations, and fees for affiliations with other labor organizations. The Grand Lodge computes the rebate based on information submitted by subordinate units and on reports submitted by Grand Lodge personnel concerning time and funds spent for political and ideological purposes. Any employee who believes his or her rebate inadequate may appeal directly to an independent Pub-lie Review Board authorized to make final determinations on such appeals.
In Findings of Fact and Conclusions of Law rendered after the trial, the district court held that BRAC’s voluntary rebate plan constituted a good-faith effort to comply with the requirements imposed by the United States Supreme Court in Street and Allen.
A. Appellants’ Constitutional Challenge to the Plan
Appellants challenge the court-approved plan, arguing that it does not protect their First Amendment right to abstain from contributing in the first place to the union’s political activities. The program fails to pass constitutional muster, they contend, because it allows the union to collect and retain the full amount of a protesting employees’ dues, use part of the dues for objectionable purposes, but not pay the rebate until the following year.
This claim is meritless. In Street, the court avoided adjudicating a First Amendment challenge to § 2, Eleventh of the Railway Labor Act by holding that the Act itself prohibited unions from forcing employees to support political causes which they oppose. 367 U.S. at 764, 81 S.Ct. at 1797. The Court then suggested two possible remedies to protect a dissenting employee, one of which was to provide “restitution to each individual employee of that portion of his money which the union expended, despite his notification, for the political causes to which he had advised the union he was opposed.” Id. at 775, 81 S.Ct. at 1803. (Emphasis added.) By definition, an act of restitution entails the return of something — in this case, the rebate of a portion of the protesting employees’ dues.
Abood squarely faced the constitutional issue avoided in Street and held that union members “may constitutionally prevent the Union’s spending a part of their required service fees to contribute to political candidates and to express political views unrelated to its duties as exclusive bargaining rep[1070]*1070resentative.” 431 U.S. at 234, 97 S.Ct. at 1799. Abood then cited Allen’s suggestion that a voluntary internal union remedy would be appropriate and deferred further judicial proceedings pending implementation of the plan. Id. at 240-42, 97 S.Ct. at 1802-03. The rebate remedy formulated to avoid statutory violations was thus approved to protect against constitutional violations as well.
The Ninth Circuit has also approved the concept of a rebate plan as an effective safeguard of employees’ rights. In Seay v. McDonnell Douglas Corp., 533 F.2d 1126, 1131 (9th Cir. 1976), the court acknowledged that a rebate plan adopted the procedure outlined in Allen, and then held that the district court (Pregerson, J.) erred in granting summary judgment solely because there was a disputed question of fact whether the union would administer the rebate program in good faith. Id. at 1132. In the instant case, the fairness of the plan has been fully litigated.4 The district court found that BRAC’s rebate plan vindicated plaintiffs’ rights. No showing has been made that this finding was clearly erroneous, and we refuse to disturb it.
B. The Standard of Proof Issue
Appellants next assert — apparently with respect both to the rebate plan and Paragraph 22 expenditures — that the district court applied the wrong standard of proof. This claim is also without merit. Under Allen, supra, the union does bear the burden of proving the proportion of political to total union expenditures when employees protest the purpose of certain expenditures. 373 U.S. at 122, 83 S.Ct. at 1163. Generally in a civil case, the party with the burden of proof must persuade the trier of fact by a preponderance of the evidence. Barr Rubber Products Co. v. Sun Rubber Co., 425 F.2d 1114, 1120 (2d Cir. 1970), cert. denied, 400 U.S. 878, 91 S.Ct. 118, 27 L.Ed.2d 115. See also E. Cleary, McCormick’s Handbook on the Law of Evidence § 339 (1972). The district court applied the preponderance of evidence standard in the instant case. Appellants, however, contend that a higher standard of proof — proof by clear and convincing evidence — was required. In support of this contention they cite an unpublished opinion of the District Court of Maryland, Beck v. C. W. A., M —76-839 (D.Md.1980). The Beck case was factually analogous to this case— it, too, was a spending protest — and the Special Master applied the clear and convincing evidence test “in view of the constitutional issues involved.” However, the Beck Special Master did so relying solely on Rosenbloom v. Metromedia, Inc., 403 U.S. 29, 91 S.Ct. 1811, 29 L.Ed.2d 296 (1971), a plurality opinion which held that a certain type of libel action had to be proved by clear and convincing evidence. That holding was extremely narrow and was not intended to extend to every case involving a constitutional claim. More importantly, Rosenbloom has been overruled on that very point. Gertz v. Robert Welch, Inc., 418 U.S. 323, 94 S.Ct. 2997, 41 L.Ed.2d 789 (1974). It is true that the higher burden of proof by clear and convincing evidence is appropriate in a limited range of civil actions — for example, to prove charges of fraud and undue influence, see McCormick supra at § 340(b) — but it is incorrect to assert that the higher burden is required every time a “constitutional issue” is involved. The trial court properly applied the preponderance of the evidence standard.
C. The Accounting Challenge
Appellants next assert that the district court’s decision that the voluntary rebate plan protects their abstention rights was clearly erroneous because the court did not require the union to conform its books and records to generally accepted accounting principles. As a result, the objecting employees argue, BRAC was unable to satisfy its Allen burden of proving the proportion of political to total union expenditures.
[1071]*1071This claim is equally without merit, mediately after it imposed the burden of proof on unions, the Allen court expressly stated that “[a]bsolute precision in the calculation of such proportion is not, of course, to be expected or required; we are mindful of the difficult accounting problems that may arise.” 373 U.S. at 122, 83 S.Ct. at 1163. In this case, the district court recognized that its Paragraph 22 ruling would be appealed and thus declined to require the union to redo its recordkeeping procedures. BRAC did produce voluminous financial records and its witnesses explained the union’s accounting methods in detail. Im-
II. APPELLANTS’ CLAIM OF PROCEDURAL ERRORS
A. Termination of Discovery
Appellants argue that the court abused its discretion when it halted discovery six months prior to trial. The court knew, appellants assert, that they intended to move to compel further answers with respect to the deposition of the union’s president. They contend that BRAC obstructed efforts to obtain information throughout the discovery process. They also contend that they were left with no way to investigate the amounts of their on-going damages. Finally, they assert that the discovery ban deprived them of access to information pertaining to two of the union’s trial exhibits.
A district court has wide latitude in controlling discovery; its rulings will not be overturned in the absence of a clear abuse of discretion. Canadian American Oil Co. v. Union Oil Co. of California, 577 F.2d 468, (9th Cir. 1978), cert. denied 439 U.S. 912, 99 S.Ct. 283, 58 L.Ed.2d 258. Appellants have failed to show any such abuse of discretion. As BRAC points out, appellants conducted extensive discovery for five years, including a full two years following the court’s summary judgment ruling on Paragraph 22 expenditures. Moreover, the discovery ban was handed down on the scheduled date of the pre-trial conference; the court’s ruling was, therefore, consistent with its Local Rule 9(d), then in effect, which specified that discovery “shall be completed, if possible, prior to the pre-trial conference.”
B. Denial of Motion to Supplement the Record
Appellants contend that the trial court abused its discretion by refusing to receive post-trial evidence of a $20.00 BRAC assessment imposed on every employee to support a national strike against a different employer, the Norfolk and Western Railway. Appellants assert this expenditure should be rebated. They brought a motion to supplement the record based on F.R.Civ.P. 59, which allows the grant of a new trial on all or part of the issues under certain circumstances, and on F.R.Civ.P. 60(b)(2), which allows the court to set aside a judgment when there is newly discovered evidence which by due diligence could not have been discovered earlier. Appellants contend that the offered evidence would demonstrate that part of the court’s prospective relief — -a $1.00 per year rebate from the Local Lodges and System Board — was grossly inadequate.
A motion to reopen to submit additional evidence is addressed to the sound discretion of the trial judge. Berns v. Pan American World Airways, Inc., 667 F.2d 826, 829 (9th Cir. 1982) and cases cited therein. The denial of a motion to vacate under F.R.Civ.P. 60(b) will be reversed only upon a clear showing of abuse of discretion. United States v. Russell, 578 F.2d 806, 807 (9th Cir. 1978). The same is true with respect to a motion to supplement the record brought under F.R.Civ.P. 59. Johnson v. United States, 270 F.2d 488, 492 (9th Cir. 1959), cert. denied, 362 U.S. 924, 80 S.Ct. 678, 4 L.Ed.2d 743 (1960). We do not believe the district court abused its broad discretion. As the union points out, the costs of a strike are germane to collective bargaining since a strike is one of the central methods employed in collective bargaining for improving wages and working conditions. The assessment in question should not be included in any rebate; the trial court’s decision was therefore correct.
[1072]*1072III. THE DISTRICT COURT’S PARAGRAPH 22 RULING
In reviewing the district court’s Paragraph 22 ruling, we are faced with a definitional problem: Are the challenged union costs political-ideological expenditures that cannot be charged to protesting employees, or are such expenditures sufficiently germane to collective bargaining, so that all employees under a union shop or agency fee agreement must contribute toward their payment? A leading labor law casebook has described this issue as “the elusive problem left unresolved by the Supreme Court of defining the kinds of ‘political’ expenses which cannot lawfully be taxed against an unconsenting employee.” A. Cox, D. Bok, R. Gorman, Labor Law 1184 (1977). The district court ruled on summary judgment that, as a matter of law, protesting employees cannot be required to help defray the union’s expenditures challenged by the instant case. These conclusions of law are subject to de novo review. State ex rel. Edwards v. Heimann, 633 F.2d 886, 888 n.1 (9th Cir. 1980).
Neither the Supreme Court nor the Ninth Circuit has considered the precise issue presented here. The Supreme Court, however, has used a variety of terms to delineate the extent of the dues obligation that can properly be imposed on a dissenting employee. Appellants urge a narrow formulation of the dues requirement based on a statement in Street that “§ 2, Eleventh [of the Railway Labor Act] contemplated compulsory unionism to force employees to share the costs of negotiating and administering collective agreements, and the costs of the adjustment and settlement of disputes.” 367 U.S. at 764, 81 S.Ct. at 1797. Without explanation, appellants contend that this statement demonstrates the Court’s intent to restrict a dissenting employee’s support obligation to those specific union functions.
Language in other Supreme Court decisions supports a broader concept of collective bargaining. Allen refers to the obligation to support “activities germane to collective bargaining,” 373 U.S. at 122, 83 S.Ct. at 1163 (emphasis added); Abood cited that language with approval, 431 U.S. at 239 n.40, 97 S.Ct. at 1802 n.40. Hanson noted that an employee has the duty to support the “work of the union in the realm of collective bargaining.” 351 U.S. at 235, 76 S.Ct. at 719 (emphasis added). Hanson also acknowledged that Congress has the power “to require ... the beneficiaries of trade unionism to contribute to its costs,” id., and specifically upheld “the requirement for financial support of the collective-bargaining agency by all who receive the benefits of its work.” Id. at 238, 76 S.Ct. at 721. These words support a broader definition of the collective bargaining concept than that urged by appellants..
Abood recognized that “[t]here will, of course, be difficult problems in drawing lines between collective-bargaining activities, for which contributions may be compelled, and ideological activities unrelated to collective bargaining, for which such compulsion is prohibited.” 431 U.S. at 236, 97 S.Ct. at 1800. In Abood, because the issues had not been fully briefed, the court declined to determine which of the activities in question might fall outside the union’s duties as exclusive bargaining representative or involve constitutionally protected rights of association. 431 U.S. at 236 n.33, 97 S.Ct. at 1800 n.33.
Supreme Court decisions thus have avoided delineating the boundaries of acceptable mandatory dues provisions in collective bargaining agreements. Circuit court decisions are equally silent on the subject. Based on our reading of Hanson, Allen, and Abood, however, we believe that the relevant inquiry is whether a particular challenged expenditure is germane to the union’s work in the realm of collective bargaining. This formulation respects and protects dissenters’ rights, but does not needlessly weaken the union, whose viability is necessary to secure and maintain industrial peace.5 Applying this test, we be[1073]*1073lieve that the district court was incorrect in holding that protesting employees cannot be charged for the union’s operating expenditures at issue here. We now turn to an item-by-item analysis of the expenditures involved in this case.
A. Grand Lodge Conventions
BRAC represents 200,000 employees throughout the country. The Grand Lodge is either in charge of or directly involved in negotiating the collective bargaining agreements pertaining to most of those employees. The quadrennial convention is an important forum for rank and file participation in determining the Grand Lodge’s collective bargaining policies. For example, the major portion of a recent convention was devoted to reports, debates, and voting on contract bargaining, grievance handling, and employee wage and benefit issues. Other significant items of business included the election of national officers and decisions concerning the union’s internal structure and fiscal management. Such activities guide the union’s approach to collective bargaining and are directly related to its effectiveness in negotiating labor agreements.6
B. Grand Lodge Litigation
Paragraph 22 exempts the vast majority of the union’s litigation expenditures from protesting employees' dues obligations. While the exempted cases did not pertain to any specific collective bargaining agreement or grievance, they did involve such things as: the union’s challenge to the legality of the airline industry’s Mutual Aid Pact, under which a struck carrier receives substantial financial assistance from non-struck carriers; the protection of employees’ rights during bankruptcy proceedings involving an employer; the doctrine of fair representation; and the defense of suits alleging violation of the non-discrimination requirements of Title VII.
The aim of the Mutual Aid Pact litigation was to strengthen the union’s ultimate collective bargaining weapon — the ability to engage in an effective strike, which is thwarted considerably if the struck carrier continues to receive substantial income from non-struck carriers.
[1074]*1074In several cases, BRAC’s intervention in an employer’s bankruptcy proceedings protected the union members’ wages and ensured continued compliance with the collective bargaining agreement while the employer underwent reorganization.
The district court’s ruling would give objecting employees a free ride as to these non-political expenses, which are related to the union’s work as the collective bargaining agent.
C. Grand Lodge Publications
The monthly magazine of the Grand Lodge is the union’s primary means of communicating information concerning collective bargaining, contract administration, and employees’ rights to employees represented by BRAC. Recent articles have reported the initiation and outcome of negotiations, explained contract demands, announced a strike ballot, and discussed issues involved in a potential strike. In addition, the magazine reports on significant events for individual System Boards — including the announcement of a pact with Western Airlines. The publication also has given advice concerning unemployment and health benefits, annuity rights, and insurance. While the magazine also includes general and recreational materials to make it more readable, that fact does not detract from the publication’s value in the collective bargaining process. It would be extremely difficult for a union to represent employees without .an effective means of communication.
D. Grand Lodge Social Activities
The union purchases refreshments for business meetings and occasional social activities, which are open to non-member agency fee payers as well as union members. Only miniscule amounts of money— approximately .70 of one percent of Grand Lodge expenditures — are involved. These small expenditures are important to the union’s members because they bring about harmonious working relationships, promote closer ties among employees, and create a more pleasant environment for union meetings. For these reasons, we believe that these costs are germane to the work of the union in the realm of collective bargaining.
E. Grand Lodge Death Benefits
Death benefit plans have historically played an important role in labor organizations. Indeed, many unions originated as mutual benefit societies.
In addition, insurance benefits are a mandatory subject of collective bargaining. Allied Chemical Workers v. Pittsburgh Plate Glass, 404 U.S. 157, 92 S.Ct. 388, 30 L.Ed.2d 341 (1971). If BRAC chooses to provide death benefits itself for all employees, rather than to seek such benefits from the employer, it is then in a better position to negotiate for additional benefits or higher wages.
Moreover, the negative consequences of permitting employees to withdraw from participation in the program are potentially quite great. If low-risk employees — the younger, healthier employees with longer life spans — could opt out, the financial stability of the program would be threatened by the number of claims coming from the remaining high-risk, older employees. Thus, provision of a death benefits plan, which tends to strengthen the employees’ ties to the union, is germane to the work of the union within the realm of collective bargaining.
F. Grand Lodge Organizing Efforts
Maximum organization of an industry benefits employees and units already organized. A union is considerably strengthened if it eliminates competition from non-union employers and a stronger union is unquestionably a more effective collective bargaining agent. Successful organizing efforts thus can strengthen the union’s position at the collective bargaining table immeasurably.
CONCLUSION
As the above discussion demonstrates, each of the challenged expenditures can be seen to promote, support or maintain the union as an effective collective bargaining [1075]*1075agent and therefore such expenditures are germane to the work of the union in the realm of collective bargaining. The district court is instructed to enter judgment in favor of BRAC and to conduct any further proceedings necessary to comply with this opinion.
AFFIRMED in part; REVERSED in part; REMANDED.