
611 F.3d 880 (2010)
UNITED STATES of America, Plaintiff-Appellant,
v.
Abelardo Ernest CRUZ, Nations Business Center, Inc., Nations Tax Services, Inc., Ruth Real, Ruth Real & Associates, Inc., Defendants-Appellees.
No. 09-11418.
United States Court of Appeals, Eleventh Circuit.
July 16, 2010.
*881 Marion E.M. Erickson, Bruce R. Ellisen, Dept. of Justice, Tax Dic., Washington, DC, for Plaintiff-Appellant.
David M. Garvin, David M. Garvin, P.A., Miami, FL, for Defendants-Appellees.
Before O'CONNOR,[*] CARNES and ANDERSON, Circuit Judges.
O'CONNOR, Associate Justice (Ret.):
Section 7407 of Title 26 of the United States Code permits the United States to seek, and a district court to issue, an injunction prohibiting tax preparers from engaging in certain deceptive or fraudulent practices. 26 U.S.C. § 7407. The district court may specifically enjoin a tax preparer from engaging in a variety of deceptive practices, including misrepresenting his eligibility to practice before the Internal Revenue Service ("IRS"). § 7407(b)(1)(A)-(D), (b)(2). If the district court finds that the tax preparer has continuously engaged in offensive conduct, and that an injunction specifically prohibiting such conduct would not be effective at preventing further abuses, "the court may enjoin such person from acting as a tax return preparer" altogether. § 7407(b)(2).
In this case, the Government brought a suit against Abelardo Ernest Cruz and four co-defendants seeking to enjoin them from operating as tax return preparers. The complaint alleged that the defendants engaged in a fraudulent tax preparation scheme in which they would intentionally overstate deductions and credits on their clients' tax returns in an effort to reduce their clients' tax liabilities and increase their refunds. It further alleged that the defendants made various misrepresentations regarding their eligibility to practice before the IRS.
*882 The District Court found that the defendants had engaged in deceptive practices in preparing tax returns and issued an injunction specifically prohibiting them from further engaging in any such conduct. It declined to completely bar them from operating as tax return preparers, as the Government requested, finding such an extreme measure was unwarranted under the circumstances of the case. The District Court also denied a post-judgment motion filed by the Government seeking to require the defendants to notify their clients of the Court's injunction.
The Government now brings this appeal. It argues that the District Court abused its discretion when (1) it did not completely enjoin defendants from acting as tax return preparers, and (2) it refused to require defendants to notify their customers of the injunction. We find that the District Court was within its discretion in finding that such a broad injunction was not warranted under the facts of this case. But because the District Court failed to give any reasons for rejecting the request to compel defendants to notify their customers of the Court's injunction, we remand for consideration of that proposal.

I
Abelardo Ernest Cruz is a tax preparer in Miami, Florida. He is the manager of Nations Business Center, Inc. ("NBC"), a company that was primarily engaged in tax return preparation through the end of 2004. In 2003, IRS Agent Alice Denny requested a full investigation of Cruz and NBC. As support for her request, Agent Denny alleged that NBC's clients were receiving refunds and claiming earned-income tax credits at rates far exceeding the national average. Agent Denny's request was eventually approved and the investigation was assigned to IRS Agent Joann Leavitt in September, 2004. Leavitt notified Cruz of the investigation and held an initial meeting with him on September 27, 2004.
Shortly after this meeting, Cruz formed Nations Tax Service, Inc. ("NTS"), and it replaced NBC as Cruz's main tax preparation service entity. In addition to her initial investigation of Cruz and NBC, Agent Leavitt's investigation eventually broadened to cover NTS, Ruth Real (an employee of both NBC and NTS), and Ruth Real and Associates ("RRA"), a small tax-return company owned and operated by Real. During the investigation, the IRS audited and analyzed 224 returns prepared by the defendants from tax years 2003 through 2006 (46 from 2003, 86 from 2004, 61 from 2005, and 31 from 2006). See United States v. Cruz, 618 F.Supp.2d 1372, 1383 (S.D.Fla.2008).[1] A few of the returns were selected for examination at random, but a majority of them were selected because they featured large or questionable deductions or exclusions.
Based on the results of the audits, which revealed numerous and repeated understatements of tax liability, the Government asked the District Court to enjoin the defendants from: (1) preparing, filing, or assisting in the preparation or filing of any federal income tax return for any other person or entity; (2) providing tax advice or services for compensation; (3) engaging in conduct subject to penalty under 26 U.S.C. §§ 6694 or 6701; and (4) engaging in any conduct that interferes with the *883 proper administration and enforcement of the internal revenue laws through the preparation or filing of false tax returns. It also asked the District Court to require defendants, at their own expense, to mail a certified copy of the Court's final injunction to their customers from previous years.
After a nine-day bench trial, the District Court determined that defendants had in fact prepared income tax returns that included unjustifiable deductions and credits, thereby artificially inflating the returns owed to their clients. The District Court focused on eleven distinct types of violations that recurred, albeit with decreasing frequency, over the four-year span covered by the investigation, as represented by the following chart:[2]


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                             Number of     Number of     Number of     Number of
                             returns in    returns in    returns in    returns in
                             2003 sample   2004 sample   2005 sample   2006 sample
                             (percent      (percent      (percent      (percent
                             of total)     of total)     of total)     of total)
-----------------------------------------------------------------------------------
Total returns                46            86            61            31
-----------------------------------------------------------------------------------
Schedule C depreciation      23 (50%)      23 (27%)      4 (6.6%)      0 (0%)
-----------------------------------------------------------------------------------
Schedule C expenses          24 (52%)      37 (43%)      17 (29%)      5 (16%)
-----------------------------------------------------------------------------------
Earned income credit         10 (22%)      18 (21%)      11 (18%)      1 (3.2%)
-----------------------------------------------------------------------------------
Child tax credit             11 (24%)      14 (16%)      6 (9.8%)      1 (3.2%)
-----------------------------------------------------------------------------------
Add'l child tax credit       7 (15%)       20 (23%)      10 (16%)      1 (3.2%)
-----------------------------------------------------------------------------------
Education credit             7 (15%)       7 (8.1%)      N/A           0 (0%)
-----------------------------------------------------------------------------------
Casualty/theft loss          N/A           N/A           17 (28%)      4 (13%)
-----------------------------------------------------------------------------------
Foreign-earned income        N/A           10 (12%)      6 (9.8%)      0 (0%)
exclusion (§ 911)
-----------------------------------------------------------------------------------
Employee business expenses   8 (17%)       16 (17%)      7 (11%)       0 (0%)
-----------------------------------------------------------------------------------
Schedule E expenses or       13 (28%)      15 (17%)      4 (6.6%)      N/A
flow-through
-----------------------------------------------------------------------------------
Form 4797 loss               3 (6.5%)      5 (5.8%)      2 (3.2%)      0 (0%)
-----------------------------------------------------------------------------------

The District Court concluded that many of these errors directly contravened the Internal Revenue Code, and that the defendants "knew or should have known" that they were claiming improper deductions. Id. at 1387. The District Court also found that the defendants had "misrepresented their eligibility to practice before the IRS." Id. at 1389.
The District Court concluded that the repeated violations warranted an injunction under 26 U.S.C. §§ 7402(a), 7407, and 7408, but that the requested injunction, barring defendants from preparing any tax returns or providing any tax advice, amounted to "the business death penalty" and was not warranted under the circumstances. Id. at 1392. In declining to issue the requested injunction, the District Court found that the evidence did not support the allegation that defendants were engaged in an ongoing pattern of fraudulent conduct, and that defendants had "clearly made a good faith effort toward eliminating the kinds of errors" they had made in the past. Id. at 1391.
The District Court particularly focused on the various new policies Cruz had implemented at NTS, created just after Cruz learned of the IRS investigation into his *884 tax preparation practices, all targeted at improving quality control and tax compliance. For instance, NTS required the person who prepared each tax return to sign it as the tax preparer, in contrast to NBC's policy of having Cruz sign each return, including those he did not personally prepare. This change, according to Cruz, would help trace errors back to their original source. NTS required its employees to complete an online tax course each semester, and Cruz himself began to personally attend annual education seminars sponsored by the IRS. NTS required each of its clients to attest that their returns were prepared using information supplied by them, and acknowledge that it was the taxpayer's responsibility to provide accurate information. The taxpayer was also required to sign every page of the return. According to the District Court, these safeguards went beyond those typically used by tax return preparers. Id. at 1386.
The District Court's judgment enjoined defendants from engaging in various types of fraudulent or deceptive conduct in their work as tax preparers and authorized the Government to continue to monitor the defendants' compliance with the injunction through post-trial discovery motions. The District Court found this injunction was "sufficient to prevent further unlawful conduct." Id. at 1374. It concluded its opinion with a warning: "Should Defendants engage in the conduct enjoined by the Court, not only will they be in violation of the law, they will be in violation of this Court's Order. Different facts will surely make for a different outcome." Id. at 1392.
The Government filed a post-judgment motion asking the District Court to amend its judgment to require the defendants to mail a copy of the Court's injunction to every customer who had used their tax preparation services in the previous five tax years, and the District Court denied the motion without comment.

II
The Government now brings this appeal, arguing that the District Court abused its discretion when it failed to completely enjoin defendants from operating as tax return preparers and when it denied the post-judgment motion seeking to have defendants notify their clients of the Court's injunction. We address each of these claims in turn.

A. Failure to Issue the Requested Injunction
The Government argues that the District Court abused its discretion when it failed to completely enjoin the defendants from operating as tax return preparers. While the Government filed its suit under 26 U.S.C. §§ 7402(a), 7407, and 7408, it focuses this first claim of error on § 7407, which explicitly authorizes district courts to completely enjoin tax return preparers from operating if certain conditions are met. To understand the preconditions § 7407 places on issuing such a far-reaching injunction, we briefly review the statute.
Section 7407(b)(1)(A) provides that a district court may issue an injunction if it finds that a tax return preparer has "engaged in any conduct subject to penalty under section 6694 or 6695 [of title 26], or subject to any criminal penalty provided by this title." 26 U.S.C. § 7407(b)(1)(A). The District Court in this case found that the defendants did engage in conduct in violation of 26 U.S.C. § 6694(a), which bars a tax preparer from understating tax liability based on unrealistic or unreasonable positions, a finding that no party contests here. Similarly, § 7407(b)(1)(B) provides that a district court may issue an injunction *885 if it finds that a defendant "misrepresented his eligibility to practice before the Internal Revenue Service, or otherwise misrepresented his experience or education as a tax return preparer." 26 U.S.C. § 7407(b)(1)(B). The District Court found that the defendants did misrepresent their eligibility to practice before the IRS and, again, no party contests that finding here.
Once a district court determines that a defendant has violated one of the prohibitions contained in § 7407(b)(1)(A)-(D) (and the defendants in this case indisputably violated two of those prohibitions), the question turns to the appropriate relief, which is addressed in § 7407(b)(2). This provision provides that a district court may enjoin a tax preparer "from further engaging in [the offensive] conduct" if the court finds that "injunctive relief is appropriate to prevent the recurrence of such conduct." 26 U.S.C. § 7407(b)(2). That is precisely the relief the District Court granted in this case when it issued an injunction prohibiting the defendants from engaging in specific types of deceptive and fraudulent conduct.
This section further provides the following, which is at the center of the dispute here:
If the court finds that a tax return preparer has continually or repeatedly engaged in any conduct described in subparagraphs (A) through (D) of this subsection and that an injunction prohibiting such conduct would not be sufficient to prevent such person's interference with the proper administration of this title, the court may enjoin such person from acting as a tax return preparer.
Id. (emphasis added). The District Court declined to enjoin defendants from operating as tax return preparers under this provision because it found that its more limited injunction was sufficient to prevent any further violations. It stressed the good faith efforts of defendants to reform their practice, as evidenced by the notable decline in the number and rate of errors in each of the eleven problem areas highlighted in the chart above.
In attacking this ruling the Government acknowledges that this Court reviews the scope of a district court's injunction for an abuse of discretion. See Angel Flight of Ga., Inc. v. Angel Flight Am., Inc., 522 F.3d 1200, 1208 (11th Cir.2008). The Government posits that the District Court based its decision to deny its requested injunction upon three clearly erroneous factual findings. See United States v. Frazier, 387 F.3d 1244, 1276 n. 12 (11th Cir.2004) ("An abuse of discretion arises when the district court's decision rests upon a clearly erroneous finding of fact." (quotation and citation omitted)). The three purported clearly erroneous findings are: (1) the District Court's finding that defendants' conduct was improving, (2) the finding that improved procedures and educational efforts would prevent future errors, and (3) that a specific-conduct injunction would be sufficient to thwart future violations. In our view, none of these three findings was clearly erroneous.
First, the District Court correctly relied upon the fact that each of the eleven errors outlined in the chart above decreased dramatically from 2003 to 2006, after the defendants realized the IRS was investigating them and after NTS implemented new quality control measures. The only errors that the District Court determined were based on unreasonable positions, in violation of § 6694(a), were occurring with decreasing frequency. The District Court appropriately concluded from this evidence that the defendants had significantly reformed their deceptive practices.
*886 The Government argues that the rate of these specific errors is of little import because the average tax loss on the audited returns, i.e., the average amount of understated tax liability, actually increased during most of the years immediately following the initiation of the IRS investigation. Those average losses were $7,659 in 2003, $7,859 in 2004, $9,711 in 2005, and $5,621 in 2006. But the problem with looking to the average tax loss, rather than the decline in the rate of certain errors, is that the relevant inquiry for the District Court was whether the defendants' violations under § 7407(b)(1) had abated. And, as described above, § 7407(b)(1)(A) only proscribes understatements of tax liability that are based on a tax preparer's unreasonable positions (or those that it knows to be wrong). So while there was evidence that the defendants continued to understate their clients' tax liabilities in the years immediately following the initiation of an IRS investigation, the Government cannot directly tie those understatements to unreasonable positions as prohibited by the statute. And the Government does not point to any error attributable to an unreasonable position taken by the defendants that increased during the course of its investigation. Nor does it point to a new type of scheme that only appeared after the investigation started.
Absent such direct evidence, it was not clearly erroneous for the District Court to conclude that the defendants' violations under § 7407(b)(1) had abated, even when the average tax loss was not on the decline. This is especially true where, as here, the average tax losses in tax returns prepared by the defendants approximated the average tax losses in all tax returns audited nationally during the relevant years, as the District Court pointed out. Cruz, 618 F.Supp.2d at 1381-83. While it is quite possible that the continued underreporting in the defendants' tax returns is attributable to some unreasonable position, the District Court did not clearly err in failing to draw such an inference absent evidence to that effect.
Second, the Government claims that the District Court clearly erred when it found that the improved procedures and educational efforts by the defendants would prevent future errors, because such procedures could not logically alleviate intentional errors. In other words, because intentional errors cannot be attributed to ignorance of the law, no amount of education will cure such errors. This argument relies on a misreading of the District Court's opinion, which concluded that the defendants "knew or should have known that they were claiming" improper deductions, id. at 1388 (emphasis added), and there is clearly nothing illogical about finding that educational efforts could lessen the number of negligent errors. While the District Court also stated, in the introduction to its opinion, that the defendants "have knowingly taken unreasonable positions on tax returns," id. at 1374, this single reference cannot bear the weight the Government seeks to place on it. In the body of its opinion, the District Court found that the defendants violated § 6694(a), proscribing the understatement of tax liability due to unrealistic positions; it never found any violation of § 6694(b), which proscribes willful, reckless, and intentional understatements of liability. And even if we agreed with the Government's reading of the District Court's opinion, there is nothing illogical in finding that educational programs could curb negligent misconduct while relying on the added sanctions of the District Court's limited injunction to curb any excess of intentional misconduct.
Third, the Government argues that it was clearly erroneous to conclude that *887 the specific-conduct injunction entered in this case would be sufficient to thwart future violations by the defendants. It would be at least somewhat odd to rule that a district court's prediction about a party's future behavior in response to a court order is clearly erroneous, so it is unsurprising that the Government's argument on this third point boils down to a legal claim: that the "District Court in this case improperly considered the traditional equitable factors in considering whether and to what extent to grant injunctive relief." Brief for the United States at 57. In other words, the Government argues that "if the statutory requirements [of § 7407] are met then a court should issue an injunction without applying traditional equitable factors." Id. This argument is untenable under § 7407(b)(2)'s plain language, which states that a district court "may enjoin" persons from acting as tax return preparers if the statutory prerequisites are satisfied, not that it "shall" or "must" issue such an injunction. The argument has also been squarely rejected by several of this Court's cases addressing parallel statutory provisions. See United States v. Ernst and Whinney, 735 F.2d 1296, 1301 (11th Cir.1984) ("[T]he decision to issue an injunction under § 7402(a) is governed by the traditional factors shaping the district court's use of the equitable remedy."); Klay v. United Healthgroup, Inc., 376 F.3d 1092, 1098 (11th Cir.2004) ("[W]hen Congress authorizes injunctive relief, it implicitly requires that the traditional requirements for an injunction be met in addition to any elements explicitly specified in the statute.").
The District Court acted within its discretion when, based on its conclusion that its limited injunction will be effective at preventing future violations, it declined to issue the broader injunction requested by the Government. It did not rely on any clearly erroneous factual finding in exercising that discretion.

B. Failure to Require Defendants to Notify Their Customers of the Injunction
In both its initial complaint and in its post-judgment motion to amend, the Government asked the District Court to require defendants to notify their customers of the Court's final injunction. The District Court did not mention this request in its initial opinion, and it denied the defendants' post-judgment motion to amend without comment. We cannot say that the District Court properly exercised its discretion in denying this request, nor can we say that it abused its discretion, given the District Court's lack of stated reasons for denying the request. We therefore vacate the judgment in part and remand the case to the District Court to reconsider this request, make appropriate findings, and explain the reasoning behind the decision it reaches on remand. See Gilmere v. City of Atlanta, 864 F.2d 734, 742 (11th Cir.1989) (vacating and remanding where district court's failure to explain reasoning in awarding fees made informed review impossible). In our view, the reasons in favor of requiring defendants to notify their customers of the injunction are substantial and merit full consideration by the District Court in the first instance.

III
The District Court's judgment is AFFIRMED in part, and VACATED and REMANDED in part.
NOTES
[*]  Honorable Sandra Day O'Connor, Associate Justice of the United States Supreme Court (Ret.), sitting by designation pursuant to 28 U.S.C. § 294(a).
[1]  The District Court's opinion repeatedly states the number of audited returns as 149, in an apparent reference to Government exhibits 81 and 82, which were admitted during Agent Leavitt's direct testimony. But the District Court's analysis clearly focuses on the updated spreadsheets introduced during the cross-examination of Agent Leavitt, defense exhibits 23-26, which included 224 audits. See 618 F.Supp.2d at 1383 (synthesizing and citing to defense exhibits 23-26 in drawing its conclusions).
[2]  This chart is reproduced from the District Court's opinion in this case, and as indicated there, items marked "N/A" did not appear in the relevant exhibits. Id. at 1383.
