From Fox v. Vice, 131 S. Ct. 2205 (2011) (decided under Civil Rights Act attorneys' fees provision, 42 U.S.C. § 1988, but logically applicable to any sanctions provision authorizing award of “reasonable attorney's fees” — e.g., Rule 11):

Federal law authorizes a court to award a reasonable attorney's fee to the prevailing party in certain civil rights cases. See 42 U.S.C. § 1988. *** We hold today that a court may grant reasonable fees to the defendant in this circumstance, but only for costs that the defendant would not have incurred but for the frivolous claims. A trial court has wide discretion in applying this standard. But here we must vacate the judgment below because the court used a different and incorrect standard in awarding fees.

***Fox's complaint asserted both state-law claims, including defamation, and federal civil rights claims under 42 U.S.C. § 1983, including interference with his right to seek public office. Vice and the town (Vice, for short) removed the case to federal court on the basis of the § 1983 claims.

At the end of discovery in the suit, Vice moved for summary judgment on Fox's federal claims. Fox conceded that the claims were "no[t] valid," App. 169, and the District Court accordingly dismissed them with prejudice. In the same ruling, the court declined to exercise supplemental jurisdiction over the remaining state-law claims.... The court instead remanded the now slimmed-down case to state court for adjudication. In doing so, the District Court observed that "[a]ny trial preparation, legal research, and discovery may be used by the parties in the state court proceedings." ***

The statute involved here, 42 U.S.C. § 1988, allows the award of "a reasonable attorney's fee" to "the prevailing party" in various kinds of civil rights cases, including suits brought under § 1983. Most of our decisions addressing this provision have concerned the grant of fees to prevailing plaintiffs. When a plaintiff succeeds in remedying a civil rights violation, we have stated, he serves "as a 'private attorney general,' vindicating a policy that Congress considered of the highest priority." ***Fee shifting in such a case at once reimburses a plaintiff for "what it cos[t] [him] to vindicate [civil] rights," *** and holds to account "a violator of federal law," Christiansburg, 434 U.S., at 418, 98 S. Ct. 694, 54 L. Ed. 2d 648.

In Christiansburg, we held that § 1988 also authorizes a fee award to a prevailing defendant, but under a different standard reflecting the "quite different equitable considerations" at stake.... In enacting § 1988, we stated, Congress sought "to protect defendants from burdensome litigation having no legal or factual basis." ... Accordingly, § 1988 authorizes a district court to award attorney's fees to a defendant "upon a finding that the plaintiff's action was frivolous, unreasonable, or without foundation."...

These standards would be easy to apply if life were like the movies, but that is usually not the case. *** [I]n the real world, litigation is more complex, involving multiple claims for relief that implicate a mix of legal theories and have different merits. Some claims succeed; others fail. Some charges are frivolous; others (even if not ultimately successful) have a reasonable basis. In short, litigation is messy, and courts must deal with this untidiness in awarding fees.

Given this reality, we have made clear that plaintiffs may receive fees under § 1988 even if they are not victorious on every claim. *** The fee award, of course, should not reimburse the plaintiff for work performed on claims that bore no relation to the grant of relief: Such work "cannot be deemed to have been expended in pursuit of the ultimate result achieved." ... But the presence of these unsuccessful claims does not immunize a defendant against paying for the attorney's fees that the plaintiff reasonably incurred in remedying a breach of his civil rights.

Analogous principles indicate that a defendant may deserve fees even if not all the plaintiff's claims were frivolous. In this context, § 1988 serves to relieve a defendant of expenses attributable to frivolous charges. The plaintiff acted wrongly in leveling such allegations, and the court may shift to him the reasonable costs that those claims imposed on his adversary. See Christiansburg, 434 U.S., at 420-421, 98 S. Ct. 694, 54 L. Ed. 2d 648. That remains true when the plaintiff's suit also includes non-frivolous claims. The defendant, of course, is not entitled to any fees arising from these non-frivolous charges. See ibid. But the presence of reasonable allegations in a suit does not immunize the plaintiff against paying for the fees that his frivolous claims imposed.***

The question then becomes one of allocation: In a lawsuit involving a mix of frivolous and non-frivolous claims, what work may the defendant receive fees for? Vice concedes, as he must, that a defendant may not obtain compensation for work unrelated to a frivolous claim.... Similarly, we think Fox would have to concede (once he has lost the argument that the presence of any non-frivolous claim precludes a fee award) that the defendant may receive reasonable fees for work related exclusively to a frivolous claim. The question in dispute concerns work that helps defend against non-frivolous and frivolous claims alike — for example, a deposition eliciting facts relevant to both allegations.***

Section 1988 allows a defendant to recover reasonable attorney's fees incurred because of, but only because of, a frivolous claim. Or what is the same thing stated as a but-for test: Section 1988 permits the defendant to receive only the portion of his fees that he would not have paid but for the frivolous claim. Recall that the relevant purpose of § 1988 is to relieve defendants of the burdens associated with fending off frivolous litigation.... So if a frivolous claim occasioned the attorney's fees at issue, a court may decide that the defendant should not have to pay them. But if the defendant would have incurred those fees anyway, to defend against non-frivolous claims, then a court has no basis for transferring the expense to the plaintiff. Suppose, for example, that a defendant's attorney conducts a deposition on matters relevant to both a frivolous and a non-frivolous claim — and more, that the lawyer would have taken and committed the same time to this deposition even if the case had involved only the non-frivolous allegation. In that circumstance, the work does not implicate Congress's reason for allowing defendants to collect fees. The defendant would have incurred the expense in any event; he has suffered no incremental harm from the frivolous claim. In short, the defendant has never shouldered the burden that Congress, in enacting § 1988, wanted to relieve. The basic American Rule thus continues to operate.

A standard allowing more expansive fee-shifting would furnish windfalls to some defendants, making them better off because they were subject to a suit including frivolous claims. ***

At the same time, the "but-for" standard we require may in some cases allow compensation to a defendant for attorney work relating to both frivolous and non-frivolous claims. Suppose, for example, that a plaintiff asserts one frivolous and one non-frivolous claim, but that only the frivolous allegation can legally result in a damages award. If an attorney performs work useful to defending against both, but did so only because of the defendant's monetary exposure on the frivolous charge, a court may decide to shift fees. Or similarly, imagine that the frivolous claim enables removal of the case to federal court, which in turn drives up litigation expenses. Here too, our standard would permit awarding fees for work relevant to both claims in order to reflect the increased costs (if any) of the federal forum. And frivolous claims may increase the cost of defending a suit in ways that are not reflected in the number of hours billed. If a defendant could prove, for example, that a frivolous claim involved a specialized area that reasonably caused him to hire more expensive counsel for the entire case, then the court may reimburse the defendant for the increased marginal cost. As all these examples show, the dispositive question is not whether attorney costs at all relate to a non-frivolous claim, but whether the costs would have been incurred in the absence of the frivolous allegation. The answers to those inquiries will usually track each other, but when they diverge, it is the second that matters.

We emphasize, as we have before, that the determination of fees "should not result in a second major litigation." Hensley, 461 U.S., at 437, 103 S. Ct. 1933, 76 L. Ed. 2d 40. The fee applicant (whether a plaintiff or a defendant) must, of course, submit appropriate documentation to meet "the burden of establishing entitlement to an award." Ibid. But trial courts need not, and indeed should not, become green-eyeshade accountants. The essential goal in shifting fees (to either party) is to do rough justice, not to achieve auditing perfection. So trial courts may take into account their overall sense of a suit, and may use estimates in calculating and allocating an attorney's time. And appellate courts must give substantial deference to these determinations, in light of "the district court's superior understanding of the litigation." Ibid.; see Webb v. Dyer County Bd. of Ed., 471 U.S. 234, 244, 105 S. Ct. 1923, 85 L. Ed. 2d 233 (1985). We can hardly think of a sphere of judicial decisionmaking in which appellate micromanagement has less to recommend it.