By a superseding indictment, Steven Mueffelman was charged by a federal grand jury with 15 counts of mail fraud, 18 U.S.C. § 1341 (2000), and 3 counts of wire fraud. Id. § 1343. A co-defendant, John Lombardi, pled guilty, but Mueffelman went to trial in a proceeding lasting almost a month. Reserving details and disputed issues for the discussion below, the evidence showed the following.
In the summer of 1996, Mueffelman, Lombardi and an attorney formed a business venture, using an inactive corporation whose name they changed to Commonwealth Capital Funding Corporation (“CCFC”). CCFC offered to assist persons who were poor or had low credit ratings in acquiring homes. A primary means was to be an arrangement in which CCFC purchased property selected by the client (within a designated price range) at up to 94 percent of its value and, in a paired transaction, immediately resold the property to the client for 100 percent of the value with full financing provided by a moi’tgage lender found by CCFC.
CCFC charged each client who enrolled in the program a $100 fee (doubled for couples and later upped to $125) for a credit check, plus one month’s gross income from the client. In exchange CCFC seemingly promised 100 percent (later expressed as “up to 100 percent”) financing. Only 17 of Mueffelman’s approximately 300 clients ever purchased homes; those who did purchase homes paid more for the homes than the sellers were willing to sell them for and qualified for a mortgage on the basis of their credit, without assistance from CCFC. Thus, most of CCFC’s income was from the initial fees rather than the 6 percent differential.
CCFC also claimed to offer a lease-to-purchase program which (as it was represented) would use a nonprofit entity to purchase a home with favorable financing and lease it to the client while the client cleaned up his or her credit record. If the client did so, the client would then assume the mortgage. A federal program was in place that provided insured financing under favorable terms where a nonprofit organization secured the financing and received the necessary government approvals.
CCFC attracted customers through advertising coupled with the use of so-called independent sales representatives who called upon and dealt directly with clients — receiving for themselves 30 percent of the initial client payment of one month’s gross income. Mueffelman, as president of CCFC, hired the sales force, approved the sales literature, made decisions on purchase offers and sought to arrange for financing. In the course of its operations in Massachusetts, lasting from September 1996 to August 1997, CCFC had or sought relationships with various mortgage brokers and at least one nonprofit organization.
Investigations by the Massachusetts banking authorities led in August 1997 to an injunction against Mueffelman, Lombardi and CCFC. In the months preceding the injunction, Mueffelman set about organizing a new but similar venture in Florida under a different corporate name, which proceeded to enroll clients and collect fees. Through August 1997, CCFC took in about $1.2 million in fees from its over 300 clients; the sales force was paid over *36$400,000; and Mueffelman himself received over $167,000, apart from payments from the new Florida venture.
In its indictment, the government identified a number of specific falsehoods, which it said that Mueffelman had used or approved to secure money from clients. Each of the counts of mail or wire fraud that followed in the indictment identified a particular mail or wire communication by CCFC to a particular customer on a specified date as a means by which the scheme was executed. The indictment alleged not only that CCFC was a sham but also described particular false or misleading statements.
Specifically, the indictment charged that CCFC advertised “100% financing” and “Home ownership guaranteed!!” and otherwise appeared to guarantee financing without a down payment for those with poor credit (e.g., “Bankruptcy OK”); that CCFC claimed to have established relationships with lenders and government-supported loan programs when in fact it had no such track record; and that CCFC claimed it was an “investor” when in fact it did no more than seek lenders.
At trial the government offered evidence from which the jury could have found that CCFC had no record and little prospect of finding lenders for clients with poor credit records and no money for down payments; that the advertising would naturally lead clients to think that they were getting guaranteed financing for their month’s gross income;1 and that Mueffelman continued to expand the business despite warnings from others including Lombardi as to difficulties in securing financing.
The jury convicted Mueffelman of 13 counts of mail fraud. (The government dismissed the remaining counts.) On November 1, 2004, the district court sentenced Mueffelman to 27 months in prison. Mueffelman now appeals, contesting both the jury verdict and his sentence. The standard of review varies with the issue raised, and we start with the attacks upon the judgment of conviction and then turn to the sentence.
Mueffelman does not deny in his brief that false statements to customers were made nor that he was responsible for them. His core arguments are that his conviction should be overturned because he optimistically believed that his programs would succeed; that — contrary to the indictment — his business was not a sham enterprise; and that the government’s reliance at trial on the false statements was a constructive amendment of the indictment. We begin with Mueffelman’s good-faith argument.
The mail fraud statute, so far as pertinent to this case, requires (1) a scheme to defraud or to obtain money or property by false or fraudulent pretenses; (2) the use of the mails in executing the scheme or attempting to do so; and (3) specific intent, inferred from statutory language and common law background, which excludes false statements honestly believed to be true and promises or predictions made in good faith. United States v. Cacho-Bonilla, 404 F.3d 84, 90 (1st Cir.), cert. denied, - U.S. -, 126 S.Ct. 471, 163 L.Ed.2d 358 (2005); United States v. Dockray, 943 F.2d 152, 155 (1st Cir.1991); 2 Sand et al., Modern Federal Jury Instructions ¶ 44.01 (Instruction 44-3) (2005).
*37This is a far cry from saying that Muef-felman was free knowingly to make false statements to secure money from clients because he believed that his enterprise would succeed. One can be optimistic, even with good reason, about the prospects of a business, but one still cannot, for example, sell stock by lying about the business’ past earnings or the presence of booked orders that do not exist. A prediction made in good faith may be sheltered; a statement of fact known to be false is not.2
In Dockray, we held that a good faith instruction is not required. 943 F.2d at 155. If references to good faith are made in fraud instructions, this must be done with great care. Here, the trial court’s good faith instruction, taken as a whole, could easily have led the jury to think that lies were protected if Mueffelman believed in his enterprise. The pertinent language from the instructions is reprinted in an addendum to this opinion. The instruction was thus overly favorable to Mueffelman, but the jury convicted anyway.
Mueffelman attempts on appeal to use the overbroad instruction as the yardstick by which to measure the sufficiency of the evidence against him, claiming that the instruction is “the law of the case.” It may be unhelpful to use the phrase “law of the case” in the present context, as if this court were bound by a district court’s ruling; -but, in any event, the overbroad instruction, properly objected to by the government’ and likely to be misread in Mueffelman’s favor, does not prevent us from determining the proper legal tests for scienter.3
Using the correct legal yardstick, Muef-felman is unquestionably liable for statements of fact that he had to know were untrue. Importantly, his advertising said or implied that Mueffelman’s business had been ongoing for several years, that it was in a position to secure 100 percent financing, and that it had a network of lenders willing to provide loans. Whether Muef-felman was generally optimistic about his venture does not excuse his lies.
Mueffelman’s next argument is that the government charged in the indictment that his business was from the outset a sham and failed to prove it. The indictment did so charge: paragraph 22 stated, “In short, the entire business enterprise conducted by Mueffelman and Lombardi was a sham designed solely to generate advance fees.” But the indictment also described in detail the effort to procure monies from clients by specific falsehoods which the government did prove — which, with the mailings, made out a violation of the mail fraud statute.
*38Whether the government failed to prove that the whole enterprise was a sham from start to finish is a different matter.4 The district judge said in connection with sentencing that CCFC was not a sham, relying on long hours spent by Mueffelman at the office and endless efforts to find mortgage lenders. We need not decide if the jury could rationally take a different view of the evidence, because the sham allegation did not have to be proved to permit and sustain the conviction.
The indictment adequately charged and gave notice of a series of false statements, and conviction on this basis did not constitute a “constructive amendment” of the indictment. A constructive amendment (fatal without regard to prejudice) occurs when “the charging terms of the indictment are altered, either literally or in effect, by prosecution or court after the grand jury has last passed on them,” but a variance, which is permissible unless prejudice is shown by the defendant, occurs “when the charging terms remain unchanged but when the facts proved at trial are different from those alleged in the indictment.”5
The concepts of constructive amendment and variance are closer to a continuum than exclusive categories. See Haines v. Risley, 412 F.3d 285, 291 (1st Cir.), cert. denied, — U.S. -, 126 S.Ct. 831, 163 L.Ed.2d 709 (2005). Similarly, the line between “the crime charged” and “the facts charged” is inherently fuzzy. And the distinction between the concepts is complicated by their use to achieve multiple ends: to uphold the grand jury as a safeguard, to identify the crime for double jeopardy purposes, and to give fair notice to the defense.
Here, the titular crime was not altered: Mueffelman was charged with mail fraud and convicted of mail fraud. What Muef-felman argues is that the scheme with which he was charged was to perpetrate a “sham” business and instead he was convicted only of false representations. But, of course, he was by the express terms of the indictment charged with doing both as part of the overall scheme. This is not a case where the indictment contained allegations of a sham but not false representations.
There was no constructive amendment of the indictment but only (if no sham was proved) a scheme similar to but somewhat narrower in breadth and malignity than that charged in the indictment. Stirone v. United States, 361 U.S. 212, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960), relied on by Mueffel-man, applies where the indictment was “broadened by amendment.” Id. at 215-16. By contrast, where the government proves less than alleged, the result is — at the very worst6 — a variance:
“A jury need not believe that the defendant did everything that the indictment *39charges; it may convict if it believes he did some of the things the indictment charges and if those things, by themselves, amount to a violation of the statute[,]” provided that the indictment “enable[s] the accused to know the nature and cause of the accusation against him.”
United States v. Callipari, 368 F.3d 22, 34 (1st Cir.2004), vacated on other grounds, 543 U.S. 1098, 125 S.Ct. 985, 160 L.Ed.2d 998 (2005) (quoting United States v. Doherty, 867 F.2d 47, 55 (1st Cir.1989)).
As Callipari demonstrates, a variance is fatal only if the defendant shows prejudice. Mueffelman says that, to refute the sham allegation, he chose in his cross-examination of Lombardi to bring out and adopt Lombardi’s assertions showing that the participants had not sought to perpetrate a sham. If no sham had been charged, says defense counsel, there would have been no need to rely on Lombardi and the defense would have concentrated more on refuting the charges of false representations.
The argument does not wash. Most important, the government was perfectly entitled to charge in one indictment both that the business was a sham and that it involved false representations. Only if the latter were omitted or were masked by an undue emphasis on the former charge would there be any hope of showing lack of notice. But the false statements were explicitly and extensively charged, and at trial defense counsel did seek to refute them where he could do so.
Counsel may be arguing that the charge of sham required the defense to accredit Lombardi and downplay its hostility to his adverse testimony. In fact, the sham charge opened up an opportunity to focus the defense on an issue where Mueffelman had some hope of prevailing and to downplay the false representations issue where the defense was considerably weaker. In any event, the fact that a witness might help as to one issue and hurt on another is just a “can’t help” of the litigation process.
Separately, Mueffelman attacks his sentence, which occurred in the period after Blakely v. Washington, 542 U.S. 296, 124 S.Ct. 2531, 159 L.Ed.2d 403 (2004), but before United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005). The district judge correctly anticipated that Blakely would undermine the then-existing mandatory guideline regime. She chose therefore to treat the guidelines as advisory although instructive, United States v. Mueffelman, 327 F.Supp.2d 79, 96 (D.Mass.2004) (“Mueffelman I”),7 and turned out to be right.
Under the pertinent guidelines, the base offense level for the fraud was 6, U.S.S.G. § 2F1.1(a) (1995), adjusted upward for multiple and vulnerable victims, U.S.S.G. §§ 2F1.1(b)(2), 3A1.1(b). Mueffelman II, 400 F.Supp.2d at 372. The most important adjustment was for the loss inflicted. The government argued for 11 additional levels based on an intended loss to victims of at least $1.1 million, the figure calculated by the probation report.
The resulting range, based on an offense level of 21, was 37 to 46 months. The district court, believing that the scheme had not been a sham at the outset, ruled that the loss overstated Mueffelman’s culpability and reduced the offense level to 18, yielding a range of 27 to 33 months. Mueffelman II, 400 F.Supp.2d at 379. The district court then sentenced Mueffel*40man to 27 months in prison and later entered a restitution order.
Mueffelman says that the judge’s framework for sentencing differed from the post-Booker framework as developed in United States v. Jiménez-Beltre, 440 F.3d 514, 518-19 (1st Cir.2006) (en banc). To the extent it did, it was not to Mueffel-man’s disadvantage.8 The district court judge treated the guidelines as advisory although entitled to weight, discounted the loss figure, listened to arguments made by Mueffelman for a still lower sentence, and took account of section 3553 factors to the extent argued by Mueffelman. See United States v. Dixon, 449 F.3d 194, 205 (1st Cir.2006).
Only two of those specific arguments made to the district court are renewed on appeal, and the district court’s treatment of both is easily sustained. First, Mueffel-man urged at sentencing that anything beyond a probationary sentence would impair his ability to provide restitution for victims. He proposed several arrangements, by which he would be placed on probation and earn $120,000-175,000 per year to pay toward restitution, with a friend promising to make up any short fall.
After hearing objections from the government, the district judge rejected the proposal. She said that she shared the prosecutor’s skepticism about whether the promised restitution would be forthcoming and, in addition, she deemed the case among “the most serious” she had seen in the white-collar crime category. She noted that the fraud was visited not upon a business but upon individuals whom the defendant knew personally.
Any notion that the district judge acted unreasonably would be hopeless. Restitution is desirable but so is the deterrence of white-collar crime (of central concern to Congress), the minimization of discrepancies between white-and blue-collar offenses, and limits on the ability of those with money or earning potential to buy their way out of jail. See United States v. Thurston, 456 F.3d 211, 218 (1st Cir.2006).9 We need not describe the moving testimony of victims in this case as to the effect of the fraud on their lives.
The other argument for a lower sentence that Mueffelman urged in the district court and now renews is the disparity between his sentence and the lesser sentence of his co-defendant. Lombardi, it will be remembered, pled guilty and assisted the government, which moved for a downward departure on that account. U.S.S.G. § 5K1.1 (1995). Although the government had sought some jail time in its motion for downward departure, the district court itself placed Lombardi on probation.
Our central concern with disparities is between what the defendant was given and what is done nationally with defendants in the same circumstances. Thurston, 456 F.3d at 216; United States v. Navedo-Concepción, 450 F.3d 54, 60 (1st Cir.2006); United States v. Smith, 445 F.3d 1, 5 (1st Cir.2006). In the ordinary course, a sentence within the guidelines is likely to re-*41fleet the national standard; and Mueffel-man was sentenced within the guideline range (or below it, depending on how one construes the district court’s loss reduction).
A concern could exist as to both rationality and appearance if two identically situated defendants received discrepant sentences from the same judge, United States v. Saez, 444 F.3d 15, 19 (1st Cir.2006), cert. denied, — U.S. -, 127 S.Ct. 224, 166 L.Ed.2d 178, 2006 WL 1970133 (Oct. 2, 2006), but this is hardly the present situation. That Lombardi assisted the government is a routine basis for a lower sentence, a policy endorsed in statute, guidelines and precedent. 18 U.S.C. § 3553(e) (2000) (allowing a sentence even below mandatory minimum); U.S.S.G. § 5K1.1; e.g., United States v. Duhon, 440 F.3d 711, 720-21 (5th Cir.2006).
Mueffelman’s brief implies that the exact extent of the disparity needed to be explained. It did not: where the defendant’s own sentence has been justified and the basis for a co-defendant’s lesser sentence is set forth or is apparent, no more precise calibration of the difference between them is customarily feasible, let alone required. Cf. United States v. Scherrer, 444 F.3d 91, 94-95 (1st Cir.2006) (en banc); Navedo-Concepción, 450 F.3d at 58.
Affirmed.
ADDENDUM
The third element concerns whether the defendant’s participation in the scheme was knowing and willful. To act knowingly means to act while being conscious and aware of his or her actions, realizing what he or she was doing or what was happening around him or her, and not acting because of ignorance, mistake, accident, or negligence.
To act willfully means to act voluntarily and intelligently and with the specific intent to do something that the law forbids. That is to say, with a bad purpose either to disobey or disregard the law.
To act with specific intent to defraud means to act willfully and with the specific intent to deceive or cheat for the purposes of obtaining money or other property or bringing about financial gain.
Intent or knowledge may not ordinarily be proven directly, because there is obviously no way to directly scrutinize the human mind. You may consider, in determining what the defendant knew or intended at any given time, you may consider any statements made or acts done or omitted by the defendant and any and all facts or circumstances received in evidence that may assist you. Again, circumstantial evidence.
You may infer, but you’re certainly not required to infer, that a person intends the natural and probable consequences of acts knowingly done or knowingly omitted. It is entirely up to you, however, to decide what facts are proven by the evidence that has been received in this trial.
Excuse me. I thought I could make it through without a coughing jag, but I didn’t.
Okay. Now, I’m going to talk for a moment about good faith. Since an essential element of the crime charged is intent to defraud, it follows that good faith on the part of the defendant is a complete defense for the charge of mail iraud. However, although I described this as a complete defense, the defendant, again, has no burden to establish this defense.
As in all matters, it is the government who must establish beyond a reasonable doubt that the defendant acted with specif-*42ie intent to defraud as charged in the indictment.
Even if you find that there were false statements or misrepresentations or omissions of material facts, they do not amount to fraud unless you also find that they were done with fraudulent intent.
A defendant acts in good faith when he actually believed, one, that the plan would succeed; two, that promises made be kept; and, three, that representations made would be fulfilled.
An honest belief in the truth of the representations made by a defendant at the time they were made, however inaccurate they may turn out to be, is consistent — is not consistent, rather, with an intent to defraud. Likewise, a fraudulent intent is not necessarily to be inferred from the fact that the venture was unprofitable, nor is fraudulent intent established by evidence that the person made a mistake of judgment or an error in management or was careless.
In order to establish fraudulent intent, it must be established that the person knowingly or intentionally attempted to deceive another. One who knowingly and intentionally deceives another is chargeable with fraudulent intent notwithstanding the manner and the form in which the deception occurred.