KEARSE, Circuit Judge:
Defendants American Board of Trade, Inc. (“ABT”), et al., appeal from a final judgment entered in 1985 in the United States District Court for the Southern District of New York, Vincent L. Broderick, Judge, which, inter alia, permanently enjoined defendants from engaging in certain commodity option transactions in violation of the Commodity Exchange Act, as amended (“the Act”), 7 U.S.C. §§ 1-24 (1982), and ordered defendants to disgorge $126,706 to their injured customers and to pay approximately $210,000 as the fees and expenses of a court-appointed trustee. On appeal, defendants contend principally that the district court erred in finding the Act applicable to their activities and abused its discretion in fashioning relief. Plaintiff Commodity Futures Trading Commission (“CFTC” or the “Commission”) cross-appeals, contending principally that the court should have ordered defendants to disgorge at least $434,961, representing its estimate of the profits received by defendants in their unlawful activities. For the reasons below, we affirm the judgment in all respects.
I. BACKGROUND
ABT is an organization that provided, inter alia, an exchange and marketplace for certain commodity options transactions. Defendants Arthur N. Economou (“Economou”) and Phyllis H. Economou are officers and directors of ABT. The other defendants are corporations affiliated with ABT, Economou, and Phyllis H. Economou.
CFTC commenced the present action in April 1979, alleging that defendants, none of whom was then registered with the Commission in any capacity, were engaged in the offer and sale of “put,” “call,” “standard double,” “combination double,” and “hedge double” options in gold and silver bullion, silver coins, platinum, copper, plywood, and several foreign currencies, in violation of §§ 4c(b) and 4c(c) of the Act as then codified at 7 U.S.C. §§ 6c(b) and 6c(c) (1976 & Supp. II 1978), and of Commission Regulations 32.7 and 32.11, promulgated under the Act, 17 C.F.R. §§ 32.7, 32.11. CFTC sought injunctive relief and an order requiring defendants to disgorge all benefits received from their allegedly unlawful transactions.
In their answers to the complaint, defendants admitted that they were engaged in the option transactions described in the Commission’s complaint, but denied that such transactions were subject to regulation under the Act. Economou asserted several affirmative defenses and counterclaims, which eventually were adopted by his codefendants, alleging, inter alia, that regulatory and statutory actions limiting commodity options violated defendants’ First Amendment rights, deprived them of their property without due process, and created unreasonable classifications.
The principal thrust of defendants’ statutory argument was that the Act reached only options on futures contracts, not options in spot and cash markets, i.e., options on the underlying commodities; since defendants engaged only in the latter transactions, they contended that their conduct was outside the Act. Alternatively, they contended that a sentence (the so-called “Treasury Amendment”) in § 2(a)(1) of the Act, 7 U.S.C. § 2, excluded from the Act options to buy or sell foreign currency, which were part of defendants’ business.
A. The Proceedings Leading to the Granting of the Permanent Injunction
The Commission promptly moved for and was granted preliminary injunctive relief against defendants’ continuation of their commodity options transactions. In a Memorandum Order filed on July 13, 1979, and published at Commodity Futures Trading Commission v. Economou, Am. Bd. of Trade, 473 F.Supp. 1177, the district court construed the Act, in light of its language and legislative history, to extend to options on the underlying commodities as well as options on futures contracts, and to cover options to buy and sell foreign currencies. Finding it clearly likely that defendants would continue their challenged activities unless enjoined, the court entered an order preliminarily enjoining defendants, inter alia,
(a) from accepting money, securities, or property (or extending credit in lieu thereof) from any person in connection with the purchase or sale of any commodity option; [and] (b) from soliciting and accepting orders for the purchase or sale of commodity options and from supervising persons so engaged
Id. at 1178.
In October 1981, having granted the Commission’s motion to strike defendants’ affirmative defenses and denied defendants’ motions to file amended answers on the ground that they failed to state viable constitutional defenses, the district court found that there were no genuine issues of material fact as to the unlawfulness of defendants’ activities. It therefore granted the Commission’s motion for partial summary judgment making the preliminary injunction permanent, adopting the findings of fact and conclusions of law set forth in its order granting the preliminary injunction. As incorporated into the final judgment in 1985, defendants were enjoined from
(a) offering to enter into, entering into, or confirming the execution of any commodity option transaction involving any commodity regulated under the Act;
(b) accepting money, securities or property (or extending credit in lieu thereof) from any person in connection with the purchase or sale of any commodity option;
(c) soliciting or accepting orders for the purchase or sale of commodity options, or from supervising persons so engaged; and
(d) refusing to produce for inspection by authorized representatives of the Commission records that Commission regulations require to be kept;
in violation of Sections 4c(b) and 4c(c) of the Commodity Exchange Act, as amended, 7 U.S.C. §§ 6c(b) and 6c(c) (1982), and Regulations 32.7(e) and 32.11 promulgated under the Act, 17 C.F.R. §§ 32.7(e) and 32.11 (1983).
B. The Disgorgement Order
Following the entry of its permanent injunction, the district court ruled that defendants would be required to disgorge certain sums received as a result of their unlawful transactions. A trustee was appointed, and defendants were ordered to deliver to the trustee “all premiums and other proceeds received by defendants in connection with the offer and sale, by them, of commodities options during the period June 1, 1978 to July 13, 1979.” The trustee was given authority to, inter alia, retain an accounting firm and other consultants to assist him, take testimony under oath, and examine into defendants’ books and records. He was directed to report to the court a proposal for distribution of the recovered proceeds to customers who had purchased commodity options from defendants during the period at issue.
An initial report filed by the trustee in February 1984, accompanied by an analysis made by his retained accounting firm, calculated that defendants had received premiums and other proceeds totaling at least $5.1 million. An alternative calculation of $6.3 million was also reported. The different figures represented disagreements between the parties as to the proper interpretation of the court’s order leading to the proceedings before the trustee. The district court held a hearing with respect to the trustee’s report and raised further questions with respect to the amount of profits gained by defendants from the sale of commodity options in the period specified.
In January 1985, the trustee reported back to the court that, in light of certain retractions in the testimony of defendants’ accountant there was “no way to quickly ascertain ABT’s profits from the sale of commodity options.” In a hearing convened thereafter, the court stated as follows:
While I find that there were substantial profits realized, I am satisfied that it is almost impossible, without a further extraordinary expenditure of effort and expense, to determine the amount of such profits____
What I have done, therefore, is to determine an amount of disgorgement which, under all the circumstances of this case, I determine to be equitable.
The court concluded that defendants should be required to disgorge the sum of $126,-706, representing the monetary losses suffered by their customers as a result of the unlawful transactions.
As incorporated in the final judgment, the disgorgement order provided as follows:
1. That defendants shall disgorge to the trustee the sum of $126,706, or such other sum as the court approves, as may be necessary to make whole those members of the public who lost money through the purchase of commodity options from defendants during the period ór thereafter.
2. That the defendants shall pay to the trustee, and to accountants or others retained by him in connection with the performance of his duties, the reasonable fees and expenses, in the sum of $31,-047.26 to Robert G. Morvillo, Esq. and $179,183 to Arthur Young and Co., and such other fees and expenses, as the court approves, as may reasonably be incurred by the trustee in connection with the distribution of disgorged funds to purchasers of commodity options, as described in Paragraph 1 above.
3. Defendants shall be jointly and severally liable for the payment of the disgorgement, fees and expenses set forth above.
CFTC moved for reconsideration of the court’s ruling as to the amount defendants would be required to disgorge, arguing that they should be ordered to disgorge all of the profits they received from the unlawful transactions. It contended that, conservatively estimated, defendants had netted at least $434,961 in profits. The court denied CFTC’s motion, and these appeals and the cross-appeal followed.
II. THE MERITS
In their challenge to the district court’s rulings on the merits of the Commission’s claims against them, defendants principally renew their contentions (1) that the Act did not apply to their transactions because it reached only options on commodity futures and not options on the underlying commodities, (2) that their transactions relating to foreign currency fell within the ambit of the Treasury Amendment and were therefore not subject to regulation under the Act, and (3) that regulation of their commodity option business by Congress and the Commission violated their constitutional rights. We find no merit in any of these arguments.
A. The Statutory and Regulatory Bans on Options
The Act as it existed during the period in question set out an intricate scheme of regulation of trading in options. Certain options transactions were prohibited outright. Thus, § 4c(a), 7 U.S.C. § 6c(a) (1976 & Supp. II1978), made it unlawful to enter into certain options transactions involving commodities that were specifically listed in § 2(a)(1) of the Act prior to the enactment of the Commodity Futures Trading Commission Act of 1974 (“CFTA”), Pub.L. No. 93-463, 88 Stat. 1389. Prior to the CFTA, § 2(a)(1) defined as commodities wheat, cotton, rice, and a number of other agricultural products. The commodities to which defendants’ transactions pertained were not, prior to 1974, listed in § 2(a)(1).
In 1974, the § 2(a)(1) definition of commodity was expanded by the CFTA to include “all other goods and articles, except onions ..., and all services, rights, and interests in which contracts for future delivery are presently or in the future dealt in.” Options transactions in these newly included commodities were not banned outright but were subjected to regulation or prohibition by the Commission. Thus, § 4c(b), 7 U.S.C. § 6c(b), made it unlawful to enter into transactions involving commodities regulated but not listed in 7 U.S.C. § 2 prior to the CFTA, if to do so would violate a rule or regulation of the CFTC:
(b) Commodities regulated but not specifically listed
No person shall offer to enter into, enter into, or confirm the execution of, any transaction ... involving any commodity regulated under this chapter, but not specifically set forth in section 2 of this title, prior to October 23,1974, which is of the character of, or is commonly known to the trade as, an “option”, “privilege”, “indemnity”, “bid”, “offer”, “put”, “call”, “advance guaranty”, or “decline guaranty”, contrary to any rule, regulation, or order of the Commission prohibiting any such transaction or allowing any such transaction under such terms and conditions as the Commission shall prescribe
7 U.S.C. § 6c(b) (Supp. II 1978).
In 1978, the Commission, persuaded that its attempts at less restrictive regulation had failed because “the offer and sale of commodity options has for some time been and remains permeated with fraud and other illegal or unsound practices,” 43 Fed. Reg. 16153, 16155 (Apr. 17, 1978); see also British American Commodity Options Corp. v. Bagley, 552 F.2d 482, 486-87 (2d Cir.), cert. denied, 434 U.S. 938, 98 S.Ct. 427, 54 L.Ed.2d 297 (1977), adopted a regulation banning transactions in commodity options:
(a) Notwithstanding any other provision of this Part 32, it shall be unlawful on and after June 1, 1978, until further rule, regulation or order of the Commission, for any person to solicit or accept orders for, or to accept money, securities or property in connection with, the purchase or sale of any commodity option, or to supervise any person or persons so engaged.
17 C.F.R. § 32.11. Thus, with certain exceptions not relevant here, as of June 1, 1978, all commodity options transactions were prohibited.
In the Futures Trading Act of 1978 (“1978 Act”), Congress codified the prohibition embodied in 17 C.F.R. § 32.11 by enacting a similar statutory provision effective October 1, 1978. See Pub.L. No. 95-405, 92 Stat. 865, 867. The prohibition enacted in 1978 became § 4c(c) of the Act, 7 U.S.C. § 6c(c) (Supp. II 1978), and provided in relevant part:
(c) Commodity option transaction; conditions ending prohibition; excepted persons
Notwithstanding the provisions of subsection (b) of this section, no person may, after September 30, 1978, offer to enter into, enter into, or confirm the execution of any commodity option transaction involving any commodity regulated under this chapter but not specifically set forth in section 2 of this title prior to October 23, 1974, until (1) the Commission transmits to the House Committee on Agriculture and the Senate Committee on Agriculture, Nutrition, and Forestry documentation of its ability to regulate successfully such transactions, including a copy of the Commission’s proposed rules and regulations, and (2) the expiration of thirty calendar days of continuous session of Congress after the date of such transmittal.
With certain exceptions not pertinent here, therefore, as of October 1, 1978, the Act itself prohibited transactions in all commodity options.
There is no dispute that the transactions engaged in by defendants from June 1, 1978, until they were preliminarily enjoined on July 13, 1979, were options, and that they were options on articles not listed in § 2(a)(1) prior to the CFTA. Nor is there any genuine question that the commodities on which defendants bought and sold options were commodities “in which contracts for future delivery are presently ... dealt in,” i.e., options made subject to regulation by the CFTA. By their plain terms, therefore, CFTC Regulation 32.11 as of June 1, 1978, and § 4c(c) as of October 1, 1978, prohibited defendants’ transactions.
We see no merit in defendants’ argument that the Act and the regulations did not reach their activities because defendants bought and sold options in the spot and cash markets, i.e., options on the commodities themselves rather than options on futures contracts. The terms of the statute and the regulation were all-encompassing: Section 4c(b) referred to any transaction “involving any commodity regulated under this chapter,” 7 U.S.C. § 6c(b) (emphasis added); and the prohibitions of both § 4c(c) and Regulation 32.11 applied to “any commodity option,” 7 U.S.C. § 6c(c) (emphasis added); 17 C.F.R. § 32.11 (emphasis added). The language of § 2(a)(1), including within the term “commodity” all articles or services whose futures are or will be traded, did not, as defendants would have it, suggest that, only options on futures contracts are regulated. The thrust of this definition was expansive rather than limiting. As one of our sister Circuits has stated, “[b]y [the 1974] amendment, literally anything other than onions could become a ‘commodity’ ... simply by its futures being traded on some exchange.” Board of Trade v. SEC, 677 F.2d 1137, 1142 (7th Cir.) (footnote omitted), vacated as moot, 459 U.S. 1026, 103 S.Ct. 434, 74 L.Ed.2d 594 (1982); accord 1 P. Johnson, Commodities Regulation § 1.01, at 4 (1982).
Nor do we accept defendants’ contention that the language of various cases demonstrates that Congress’s only concern was to regulate trading in options on futures contracts. See, e.g., Strobl v. New York Mercantile Exchange, 768 F.2d 22, 25 (2d Cir.) (noting, in a case involving futures manipulation, that early enactments established “the pattern of commodity futures regulation”), cert. denied, --- U.S. ---, 106 S.Ct. 527, 88 L.Ed.2d 459 (1985). The discussions in those cases focused on the factual situations at issue; and their language is not to be taken as restricting the plain language of the statute and the regulation.
We conclude that the district court did not err in finding that defendants’ commodity options transactions from June 1, 1978, to July 13, 1979, violated §§ 4c(b) and (c) of the Act and Regulation 32.11.
B. The Treasury Amendment
Defendants also contend that the district court erred in failing to hold that their option transactions relating to foreign currencies were excluded from the Act’s reach by operation of the Treasury Amendment, a sentence found in § 2(a)(1) of the Act, 7 U.S.C. § 2. That sentence read, in pertinent part, as follows:
Nothing in this chapter shall be deemed to govern or in any way be applicable to transactions in foreign currency ... unless such transactions involve the sale thereof for future delivery conducted on a board of trade.
The district court reasoned that an option to buy or sell foreign currency is not a purchase or sale of the currency itself and hence is not a transaction “in” that currency, but at most is one that relates to the currency. See 473 F.Supp. at 1182. (The court thus found it unnecessary to reach the question whether the defendants’ transactions fell within the “unless” clause of the section.) We agree. An option transaction giving the option holder the right to purchase a foreign currency by a specified date and at a specified price does not become a “transaction[ ] in” that currency unless and until the option is exercised. See Board of Trade, 677 F.2d at 1154 (relying partly on the opinion of the district court in this case); CFTC v. Sterling Capital Co., [1980-1982] Comm.Fut.L.Rep. (CCH) ¶ 21,169, at 24,783-84 (N.D.Ga.) (same), modified on other grounds, [1980-1982] Comm.Fut.L.Rep. (CCH) ¶ 21,170 (N.D.Ga.1981). Hence the Treasury Amendment did not, on its face, appear to exclude defendants’ foreign currency options business from regulation.
This interpretation of the Treasury Amendment is consistent with its legislative history. That history discloses that the exception was included in the CFTA at the behest of the Treasury Department on the ground that the protections of the Act were not needed for the sophisticated financial institutions, already subject to regulation, that participated in such transactions:
[T]he Committee included an amendment to clarify that the provisions of the bill are not applicable to trading in foreign currencies and certain enumerated financial instruments unless such trading is conducted on a formally organized futures exchange. A great deal of the trading in foreign currency in the United States is carried out through an informal network of banks and tellers. The Committee believes that this market is more properly supervised by the bank regulatory agencies and that, therefore, regulation under this legislation is unnecessary.
S.Rep. No. 1131, 93rd Cong., 2d Sess., reprinted in 1974 U.S.Code Cong. & Ad. News 5843, 5863; accord id. at 5848 (“the Committee amendment provides that interbank trading of foreign currencies and specified financial instruments is not subject to Commission regulation”) (emphasis in original); see 1 P. Johnson, Commodities Regulation § 101, at 5 & n. 4. These descriptions of the intended reach of the Treasury Amendment belie the notion that the exception was designed to exclude from regulation foreign currency options transactions such as those defendants engaged in with private individuals.
C. Defendants’ Constitutional Defenses
Defendants contend that the district court erred in dismissing their constitutional defenses to the present action. These included principally the assertions that the present suit violates their First Amendment rights and that the Act and the Commission’s regulations violate notions of substantive due process and equal protection. We conclude that the district court did not err in dismissing these claims summarily.
With respect to their First Amendment claim, it is not entirely clear whether defendants contend that the present suit is designed to punish them for their past efforts to have the Act amended or to silence them in the future, or both. In any event, defendants sought to support this claim by pointing to the following statement in a 1976 memorandum from one CFTC commissioner to another:
Economou will argue that because he is selling options on a physical commodity he is therefore not subject to the exclusive jurisdiction provisions of the CFTC. However, we will argue against this, but, even if we would fail to prevail, the end result should be the same, i.e., Economou is still subject to our regulations. Therefore, his options program should be out of business.
Defendants made no other factual allegations, relying solely on allegations that the district court accurately termed “conclusory, vague, and general.”
We agree with the district court that the memorandum does not appear to have any bearing on the claim that CFTC sought to interfere with defendants’ First Amendment rights. It speaks solely in terms of defendants’ business, the applicability of CFTC regulations to that business, the anticipated effect of those regulations, and the statutory interpretation argument Economou was expected to make. It contains no suggestion that the Commission’s concern with defendants related to defendants’ past or future exercise of their First Amendment rights or to any other impermissible factors. In the absence of any factual allegations as to specific instances of misconduct, the court properly dismissed the First Amendment claim. See San Filippo v. U.S. Trust Co., 737 F.2d 246, 256 (2d Cir.1984), cert. denied, 470 U.S. 1035, 105 S.Ct. 1408, 84 L.Ed.2d 797 (1985); Ostrer v. Aronwald, 567 F.2d 551, 553 (2d Cir.1977) (per curiam).
Nor does the fact that Economou is mentioned, as described above, in a Commission memorandum suffice to permit defendants to pursue a claim of selective prosecution, since they have failed to proffer any facts that could show that the Commission’s effort to regulate defendants was based on impermissible factors. See United States v. Moon, 718 F.2d 1210, 1229 (2d Cir.1983) (factual showing required in order to obtain pretrial discovery on claim of selective prosecution), cert. denied, 466 U.S. 971, 104 S.Ct. 2344, 80 L.Ed.2d 818 (1984).
Defendants’ contention that §§ 4c(b) and (c) of the Act and the Commission’s regulations violated their rights to substantive due process and equal protection, based on their assertion that these provisions cannot "be said to be remotely related to the objective which they were intended to secure,” is entirely frivolous. It has long been settled that in assessing a substantive due process attack on economic legislation, our inquiry “must be restricted to the issue whether any state of facts either known or which could reasonably be assumed affords support for [the legislation].” United States v. Carolene Products Co., 304 U.S. 144, 154, 58 S.Ct. 778, 784, 82 L.Ed. 1234 (1938). Indeed, “the existence of facts supporting the legislative judgment is to be presumed, for regulatory legislation affecting ordinary commercial transactions is not to be pronounced unconstitutional unless ... it is of such a character as to preclude the assumption that it rests upon some rational basis.” Id. at 152, 58 S.Ct. at 783 (emphasis added). Similar considerations inform our review of a claim that regulation of commercial activities amounts to a denial of equal protection:
When ... economic regulation is challenged solely as violating the Equal Protection Clause, this Court consistently defers to legislative determinations as to the desirability of particular statutory discriminations____ Unless a classification trammels fundamental personal rights or is drawn upon inherently suspect distinctions such as race, religion, or alienage, our decisions presume the constitutionality of the statutory discriminations and require only that the classification challenged be rationally related to a legitimate state interest.
City of New Orleans v. Dukes, 427 U.S. 297, 303, 96 S.Ct. 2513, 2517, 49 L.Ed.2d 511 (1976) (per curiam).
There can be no question here that the prevailing state of affairs in the commodities industry gave Congress an ample basis for regulation of commodity options and for empowering the Commission to issue further regulations. In British American Commodity Options Corp. v. Bagley, 552 F.2d at 485-86, we described the attributes of commodity options that lent themselves so readily to fraud and fiscal irresponsibility, and noted that this “especially hospitable environment for abuse” amply justified Congress and the Commission in concluding that the enactments there challenged were necessary. Defendants’ arguments to the contrary do no more than question the wisdom of the statutes and are more “properly addressed to the legislature, not to us.” Ferguson v. Skrupa, 372 U.S. 726, 731, 83 S.Ct. 1028, 1031, 10 L.Ed.2d 1347 (1963).
III. THE RELIEF
With respect to the relief granted by the district court, defendants contend that both the permanent injunction and the disgorgement order were an abuse of the district court’s discretion. CFTC challenges the disgorgement order as too lenient, contending that the court should have required defendants to disgorge a more substantial sum. We find all of these contentions unpersuasive.
A. The Propriety of the Permanent Injunction
In contending that the entry of a permanent injunction constituted an abuse of the court’s discretion, defendants point out that they were never charged with fraud in their options business, and they argue that the injunction deprives the public of the ability to continue investing in the options that defendants formerly offered and deprives defendants of the ability to continue in a business developed after “vast expenditures.” These arguments need not detain us long.
An injunction prohibiting a party from engaging in conduct that violates the provisions of a statute is appropriate when there is a likelihood that, unless enjoined, the violations will continue. See CFTC v. Co Petro Marketing Group, Inc., 680 F.2d 573, 582 n. 16 (9th Cir.1982); SEC v. Holschuh, 694 F.2d 130, 144-45 (7th Cir.1982); cf. CFTC v. British American Commodity Options Corp., 560 F.2d 135, 141 (2d Cir.) (preliminary injunction), cert. denied, 438 U.S. 905, 98 S.Ct. 3123, 57 L.Ed.2d 1147 (1977). A district court may properly infer a likelihood of future violations from the defendant’s past unlawful conduct. Cf. id. at 142; SEC v. Management Dynamics, Inc., 515 F.2d 801, 807 (2d Cir.1975) (“commission of past illegal conduct is highly suggestive of the likelihood of future violations”); see also Hecht Co. v. Bowles, 321 U.S. 321, 64 S.Ct. 587, 88 L.Ed.2d 754 (1944) (court’s discretion not necessarily abused by denial of injunction where violations of statute had been inadvertent and defendant had promptly and voluntarily taken steps to correct them).
We find no basis for concluding that the district court’s entry of a permanent injunction constituted an abuse of its discretion. There were no issues of fact as to the nature of defendants’ business, but merely legal questions as to the applicability of the Act and the regulations to that business. Nor was there any genuine issue as to the need for an injunction to ensure that defendants would in the future comply with the Act and the regulations. Even the cold record on appeal fairly shouts the probability that defendants would continue their operations if not enjoined. Their persistent contention that the Act did not apply to them and that the Commission’s regulations therefore could not, as a statutory matter, apply to them, their contention that regulation by Congress and the Commission violates their constitutional rights, and their adherence to other even less meritorious positions furnish no confidence that if not enjoined, defendants would refrain from the options transactions found here to violate the Act and the regulations. Indeed, the principal grounds urged in attacking the injunction — the unavailability of ABT to the public for such transactions and the inability of defendants to carry on their established business — indicate that defendants would otherwise proceed with their unlawful options business.
The fact that defendants have not been charged with fraud is immaterial. While fraudulent transactions are indeed unlawful, the Act and the regulations prohibited the options transactions at issue without regard to questions of fraud. Defendants’ manifest intent to continue their options business unless enjoined fully justified the entry of a permanent injunction against them. As incorporated in the final judgment, the injunction was carefully tailored to avoid any interference with legitimate activities. Thus, the court stated that the injunction was intended
to make it clear that the conduct which is permanently enjoined is conduct which is prohibited under the Act and the regulations thereunder. The injunction is not intended to prohibit commodity option transactions or activities which conform to the requirements of the Act and the regulations thereunder.
Amendment to Final Order of Permanent Injunction dated October 11, 1984. We conclude that defendants have failed to show any basis for disturbing the permanent injunction.
B. The Disgorgement Order
Both CFTC and defendants challenge the district court’s order requiring defendants to pay the disgorgement trustee $126,706, an amount that is expected to make whole those customers who lost money through the purchase of defendants’ commodity options. Defendants contend that they should not have been compelled to disgorge any moneys because they were not charged with fraud and they “derived no identifiable profit or ill-gotten gain from [their] operation of [the commodity options] program.” (Emphasis in original deleted.) The Commission, on the other hand, contends that its most “conservative” analysis indicates that defendants enjoyed profits totaling $434,961 in the period June 1,1978, to July 13,1979, and that the court erred in not requiring the disgorgement of at least this sum. We reject both sides’ contentions.
It is clear that the district court had the power to order disgorgement as a remedy for violations of the Act, for “the purpose of depriving the wrongdoer of his ill-gotten gains and deterring violations of law.” CFTC v. British American Commodity Options Corp., 788 F.2d 92, 94 (2d Cir.1986) (per curiam). “Disgorgement not only deprives the wrongdoer of benefits derived from unlawful conduct but it also effectuates the purpose underlying the Commodities [sic ] Exchange Act — protection of the investor.” Id. A finding of fraud is not a prerequisite. See id. (citing CFTC v. Co [Petro] Marketing Group, Inc., 502 F.Supp. 806, 819 (C.D.Cal.1980), aff'd, 680 F.2d 573 (9th Cir.1982); CFTC v. Hunt, 591 F.2d 1211, 1222-23 (7th Cir.1979)).
Normally, where the defendant has received benefits from both lawful and unlawful activities, the party seeking disgorgement must distinguish between the legally and illegally derived profits. See, e.g., CFTC v. British American Commodity Options Corp., 788 F.2d at 93. In the present case, however, both defendants and the court appear to agree that such a distinction is not practicable. Defendants argue that their profits from the unlawful transaction are not “identifiable”; the trustee appointed by the court, after making efforts to identify those profits by examination of defendants’ records and by the formal and informal solicitation of information from defendants and their accountant, reported that there appeared to be no way to quantify quickly ABT’s profits from the unlawful transactions; and the court concluded that ascertainment of such profits could not be achieved absent “extraordinary expense.” The district court found that although not quantifiable, the profits in question were “substantial”; defendants plainly cannot contradict this finding since they state that those profits are not identifiable.
In the circumstances, we conclude that defendants have failed to show any abuse of the court’s discretion in setting the amount of disgorgement at $126,706. Where the defendant’s own recalcitrance and system of recordkeeping have so obscured matters that the lawful gains cannot be distinguished from the unlawful without incurring inordinate expense, it is well within the discretion of the court to rule that the measure of disgorgement will be the more readily measurable amount of losses incurred by the defendants’ customers in the unlawful transactions. Cf. Bigelow v. RKO Radio Pictures, Inc., 327 U.S. 251, 264, 66 S.Ct. 574, 580, 90 L.Ed. 652 (1946) (the court may make “a just and reasonable estimate of the damage based on relevant data” where defendant’s own wrong forecloses a more precise computation).
Nor has the Commission established that the district court abused its discretion in failing to order a greater sum disgorged. Although the Commission correctly argues that disgorgement is not designed principally to provide a remedy for parties injured by the unlawful conduct, it is hardly improper to look to the amount of such injury when the more traditional point of reference, profits unlawfully received, is not reasonably determinable. The district court was not compelled to accept as accurate the Commission’s calculations as to defendants’ actual profits; and no basis has been suggested for concluding that the court's finding that a profit determination could not easily be made was clearly erroneous. See Anderson v. City of Bessemer City, N.C., 470 U.S. 564, 105 S.Ct. 1504, 1512, 84 L.Ed.2d 518 (1985) (“Where there are two permissible views of the evidence, the factfinder’s choice between them cannot be clearly erroneous.”).
C. The Requirement that Defendants Pay the Fees and Expenses of the Trustee
Finally, we reject as meritless defendants' contentions that the court abused its discretion in appointing a trustee, requiring defendants to pay the costs associated with that appointment, and approving such costs in an amount that exceeded the amount to be disgorged. The power to order disgorgement carries with it the power to appoint a trustee (1) to assist the court in determining the amount to be disgorged and (2) to receive and disburse the sums disgorged to the proper persons. The fees and expenses of the trustee are properly chargeable to the party that has engaged in the unlawful conduct warranting the disgorgement. See SEC v. Manor Nursing Centers, Inc., 458 F.2d 1082, 1103-05 & n. 27 (2d Cir.1972).
The need for such a trustee in the present case is underscored by the arguments made by both sides with respect to the proper amount to be disgorged. The record plainly reveals that the trustee and his retained accountants expended a great deal of effort in attempting, in the face of recalcitrance by defendants, to give the requested assistance to the court. The court found that the amount of fees and expenses requested was reasonable, and we have been presented with no sound basis for disturbing that determination.
CONCLUSION
We have considered all of the arguments advanced by each of the parties in support of their challenges to the final judgment and have found them to be without merit. The judgment of the district court is in all respects affirmed. Costs are awarded to CFTC on the appeals; each party shall bear its own costs on the cross-appeal.
. Effective January 11, 1983, the Futures Trading Act of 1982, Pub.L. No. 97-444, 96 Stat. 2294, repealed the total ban, previously found in 7 U.S.C. § 6c(a), on the trading of options on agricultural commodities specifically enumerated prior to 1974 in section 2(a)(1) of the Act. The 1982 statute made all such trading subject to regulation by the Commission.