GRABER, Circuit Judge:

After the parties settled this class action, the district court awarded Plaintiffs $989,431.08 in attorney fees, which was about $500,000 less than they had requested. The Commissioner of the United States Social Security Administration ("the federal Defendant") appeals, arguing that the fee award is too large; Plaintiffs cross-appeal, arguing that the fee award is too small. We hold that (1) the district court abused its discretion by failing to deduct from the award of fees hours that were documented inadequately or that reflected duplicative efforts or excessive staffing; (2) the district court properly considered the extent of Plaintiffs' success; (3) the cost-of-living adjustment for fees awarded under the Equal Access to Justice Act (EAJA), 28 U.S.C. § 2412, must be calculated according to the consumer price index for the year in which the fees were earned; and (4) the "prevailing market rate" is the proper measure of fees awarded under 42 U.S.C. § 1988. Accordingly, we affirm the district court's order in part, reverse it in part, and remand the matter for further proceedings.

FACTS AND PROCEDURAL BACKGROUND

Pursuant to 42 U.S.C. § 421(a), states are permitted to make determinations of eligibility for Social Security benefits, on behalf and under the supervision of the Social Security Administration (SSA). The State of Oregon has undertaken that responsibility. An Oregon agency, Disability Determination Services (DDS), administers the program, and two other state agencies, the Vocational Rehabilitation Division (VRD) and the Department of Human Services (DHS), oversee DDS's operations.

In 1994, Plaintiffs filed this class action on behalf of Oregon residents whose claims for disability benefits had been or would be denied by DDS. They named as defendants the administrators of DDS, VRD, and DHS (collectively "the state Defendants") and the federal Defendant. Plaintiffs' complaint alleged that the state Defendants had "engaged in a uniform pattern of procedural practices by which initial applications and requests for reconsideration of disability benefits are wrongfully denied." Plaintiffs also alleged that the federal Defendant had failed to monitor adequately the state Defendants' administration of the disability program. They sought declaratory and injunctive relief, as well as costs and attorney fees. Plaintiffs brought their claims against the state Defendants under 42 U.S.C. § 1983, and their claims against the federal Defendant under 42 U.S.C. § 405(g).

The state Defendants moved to dismiss Plaintiffs' § 1983 claims, arguing that they did not act under color of state law in administering the SSA's benefits program. The district court denied that motion in a published opinion. Sorenson v. Concannon, 893 F.Supp. 1469, 1484 (D.Or. 1994).

After extensive discovery and an unsuccessful mediation, the parties settled on the eve of trial, in October 1998. In the parties' settlement agreement, all Defendants agreed to a series of conditions, which fell under six general headings: "Enhanced Quality Assurance"; "Additional Disability Examiners Training And Observation"; "Systemic Measures And Related Actions"; "Plaintiffs' Representation On The Advisory Council Of The Oregon DDS"; "Open Door Policy For DDS and SSA"; and "Case Review To Ascertain Possible Systemic Problems."

Additionally, the federal Defendant agreed to pay Plaintiffs' costs and attorney fees. The relevant section of the settlement agreement provides:

Plaintiffs' Counsel are entitled to payment of reasonable attorneys' fees, reasonable expenses in prosecuting this action, and costs for efforts that materially advance this litigation, consistent with applicable legal standards. In the event that the parties cannot agree to the amount of reasonable attorneys' fees, expenses and costs as defined above, plaintiffs shall file a fee application to the Court within ninety (90) days of the effective date of this agreement.

The parties were unable to agree on the amount of attorney fees. Plaintiffs therefore filed a fee petition in district court, requesting a total of $1,446,908 for 8,298.39 hours of work by lawyers, legal assistants, and law clerks. In support of their request, Plaintiffs attached affidavits, billing sheets, and other documents. They sought hourly fees of $150 for three junior lawyers, $200 for five more experienced lawyers, and $350 for one senior lawyer.

The federal Defendant opposed Plaintiffs' request for attorney fees, asserting that the hours that Plaintiffs' lawyers had claimed were excessive, duplicative, and inadequately documented. The federal Defendant contended that Plaintiffs were entitled to no more than $267,257.47 in attorney fees. Plaintiffs then filed a response memorandum, to which they attached additional documentation and billing records.

After a hearing, the district court issued an order on May 5, 1999. In its order, the court first stated that Plaintiffs had "accomplished" their "mission" in this action, which was to improve the disability determination system in Oregon. The court then noted that Defendants also claimed to have expended more than 8,000 hours of lawyer, law clerk, and paralegal services on the action. After deducting 238 undocumented hours that Plaintiffs had attributed to a law clerk, the court allowed the remaining 8,059.44 hours that Plaintiffs had claimed.

The court then set an hourly rate. The court first noted that the hours that were attributable to Plaintiffs' claim against the federal Defendant were "capped" at $132 per hour. However, the court did not make a finding as to how many hours were related to Plaintiffs' claim against the federal Defendant. The court then concluded that, although the proposed hourly rates "vary widely among plaintiffs' counsel, . . . this was a joint effort" and all counsel would be compensated at a uniform rate of $132 per hour. The court explained its conclusion as follows:

I consider this to be a fair and reasonable approach in view of the rate of inflation over the past eight years, the fact that at least part of the attorney fee claim (against the federal defendant) is restricted to $132 per hour by the Equal Access to Justice Act, and the fact that portions of the fee request are documented inadequately and reflect duplicative efforts and excessive staffing.

(Emphasis added.)

The federal Defendant appeals, arguing that the district court should have deducted from its calculation hours that were undocumented, excessive, or duplicative. It also argues that the $132 hourly rate was too high for the hours that were attributable to the claim against it.

Plaintiffs cross-appeal, arguing that the $132 hourly rate was too low for the hours that were attributable to their claims against the state Defendants.

STANDARD OF REVIEW

This court reviews a district court's award of attorney fees for abuse of discretion. See Atkins v. Apfel, 154 F.3d 986, 987 (9th Cir. 1998) (reviewing award of fees under the Equal Access to Justice Act); Odima v. Westin Tucson Hotel, 53 F.3d 1484, 1498 (9th Cir. 1995) (reviewing award of fees under 42 U.S.C. § 1988).

DISCUSSION

I. Background

The parties' settlement agreement provides that Plaintiffs will receive "reasonable attorneys' fees . . . consistent with applicable legal standards." The parties agree on appeal that those "applicable legal standards" are found, as the district court concluded, in two statutes: the EAJA (which applies to fees attributable to the claim against the federal Defendant); and 42 U.S.C. § 1988 (which applies to fees attributable to the claims against the state Defendants).

Under both statutes, a district court's award of attorney fees must be "reasonable." "The most useful starting point for determining the amount of a reasonable fee is the number of hours reasonably expended on the litigation multiplied by a reasonable hourly rate." Hensley v. Eckerhart, 461 U.S. 424, 433, 103 S.Ct. 1933, 76 L.Ed.2d 40 (1983).

For purposes of this appeal, the main difference between an award of fees under the EAJA and an award of fees under § 1988 is the calculation of the "reasonable hourly rate." Under § 1988, a reasonable hourly rate is "calculated according to the prevailing market rates in the relevant community, regardless of whether plaintiff is represented by private or nonprofit counsel." Blum v. Stenson, 465 U.S. 886, 895, 104 S.Ct. 1541, 79 L.Ed.2d 891 (1984). The burden is on the plaintiff to produce evidence "that the requested rates are in line with those prevailing in the community for similar services by lawyers of reasonably comparable skill, experience, and reputation." Id. at 895 n. 11, 104 S.Ct. 1541. The defendant may introduce rebuttal evidence in support of a lower hourly rate.

Under the EAJA, on the other hand, attorney fees are capped by Congress. Until March 29, 1996, the statute provided that "attorney fees shall not be awarded in excess of $75 per hour unless the court determines that an increase in the cost of living or a special factor . . . justifies a higher fee." 28 U.S.C. § 2412(d)(2)(A) (1994). On March 29, 1996, the statute was amended to increase the maximum fee to $125 per hour, plus any "cost of living" and "special factor" adjustments. The $125 per hour cap applies to cases commenced on or after March 29, 1996. Contract with America Advancement Act of 1996, Pub.L. 104-121, 110 Stat. 847, 863, §§ 232(b)(1), 233 (1996) (set out as a note under 5 U.S.C. § 504); see also Kerin v. United States Postal Serv., 218 F.3d 185, 189 (2d Cir. 2000).

Under either statute, a district court that awards attorney fees must "provide a concise but clear explanation of its reasons for the fee award." Hensley, 461 U.S. at 437, 103 S.Ct. 1933. "Courts need not attempt to portray the discretionary analyses that lead to their numerical conclusions as elaborate mathematical equations, but they must provide sufficient insight into their exercises of discretion to enable us to discharge our reviewing function." Cunningham v. County of Los Angeles, 879 F.2d 481, 485 (9th Cir. 1988). "If the district court fails to provide a clear indication of how it exercised its discretion, we will remand the fee award for the court to provide an explanation." McGrath v. County of Nevada, 67 F.3d 248, 253 (9th Cir. 1995).

II. Award of Fees for Hours That Were Documented Inadequately and for Hours That Reflect Duplicative Efforts or Excessive Staffing

A. Calculation of Hours

The federal Defendant first argues that the district court overstated the number of hours that Plaintiffs "reasonably expended" on this action. Specifically, it contends that the district court should have deducted hours that were poorly documented, excessive, or the result of overstaffing. "Where the documentation of hours is inadequate, the district court may reduce the award accordingly. The district court also should exclude from this initial fee calculation hours that were not `reasonably expended.'" Hensley, 461 U.S. at 433-34, 103 S.Ct. 1933.

Here, as noted, the district court found that unspecified "portions of the fee request are documented inadequately and reflect duplicative efforts and excessive staffing." But the court did not attempt to quantify such hours and exclude them from its initial fee calculation. Instead, the court lowered the hourly rate by an unknown amount to compensate for overbilling and poor documentation. Thus, the district court awarded fees to Plaintiffs for some hours that it had found to be "documented inadequately" or "not `reasonably expended.'"

That approach does not comport with our precedent. A district court has wide latitude in determining the number of hours that were reasonably expended by the prevailing lawyers, but it must provide enough of an explanation to allow for meaningful review of the fee award. Here, it is clear from the court's order that (1) some of the 8,059.44 hours for which Plaintiffs were compensated were undocumented or unreasonable, and (2) the court adjusted Plaintiffs' hourly rate to some degree in response. But the district court failed to explain how or why the unspecified reduction in hourly rate fairly balanced the unspecified number of improperly billed hours.

In Gates v. Deukmejian, 987 F.2d 1392, 1399 (9th Cir. 1992), this court reversed and remanded an award of attorney fees. In that case, the district court had simply cut 10 percent from the plaintiffs' claimed hours, to adjust for overbilling and overstaffing. This court noted that, in complex cases, a district court "is not required to set forth an hour-by-hour analysis of the fee request" and may even reduce the award on a percentage basis. Id. Nevertheless, this court reversed the fee award because the district court had failed to provide a clear explanation "for why the ten percent across-the-board reduction, when coupled with plaintiffs' discrete billing judgments, properly compensated for plaintiffs' overbilling or duplication." Id. at 1400.

This order is less informative than the order reversed in Gates. In Gates, the order specified the size of the reduction — 10 percent — but neither set out the degree of the overbilling nor explained the relationship between the number of hours improperly billed and the size of the reduction. Here, the order does not make clear the size of the deduction in hourly fees. Nor does the order set out the degree of overbilling; the district court may have concluded that a very small number of hours were unreasonably billed, or that 50 percent of Plaintiffs' hours were undocumented or unnecessary.

Further, it is entirely possible that the improper billing practices were the responsibility of some, but not all, of the lawyers who represented Plaintiffs. The lawyers' billing statements varied in specificity and clarity, and Defendants objected to some but not all of the statements. But the district court reduced fees across the board, without reference to which lawyers were responsible for the improper billing.

We recognize that the court was faced with an unusually complicated request for fees, involving years of billing by numerous lawyers. Nevertheless, our precedent requires the district court to provide greater detail about its analysis. We remand with instructions that the district court (1) make a finding concerning the number of hours that "are documented inadequately and reflect duplicative efforts and excessive staffing," (2) make a finding as to which lawyers billed those hours, and (3) deduct those hours from its calculation of the hours that Plaintiffs' counsel "reasonably expended" on this action.

B. Extent of Plaintiffs' Success

The federal Defendant also argues that the district court abused its discretion in failing to reduce Plaintiffs' award based on the "limited success" that Plaintiffs achieved in this litigation. A district court may, in its discretion, make deductions on that basis. Hensley, 461 U.S. at 436-37, 103 S.Ct. 1933. Defendant argues that deductions are appropriate in this case, because the settlement agreement neither encompasses all the relief that Plaintiffs sought nor requires the state and federal Defendants to make all the changes to their program that Plaintiffs contemplated.

Hensley sets out a two-step process for analyzing a deduction for "limited success." The first step is to consider whether "the plaintiff fail[ed] to prevail on claims that were unrelated to the claims on which he succeeded." Id. at 434, 103 S.Ct. 1933. Claims are "unrelated" if they are "entirely distinct and separate" from the claims on which the plaintiff prevailed. Odima, 53 F.3d at 1499. Hours expended on unrelated, unsuccessful claims should not be included in an award of fees.

Here, Plaintiffs' claims all were related. All focused on improving Oregon's disability determination system. They "involve[d] a common core of facts" and were "based on related legal theories." Hensley, 461 U.S. at 435, 103 S.Ct. 1933. In such cases, "[m]uch of counsel's time will be devoted generally to the litigation as a whole. . . . Such a lawsuit cannot be viewed as a series of discrete claims." Id.

The second step of the Hensley analysis is to consider whether "the plaintiff achieve[d] a level of success that makes the hours reasonably expended a satisfactory basis for making a fee award." Id. at 434, 103 S.Ct. 1933. In answering that question, a district court "should focus on the significance of the overall relief obtained by the plaintiff in relation to the hours reasonably expended on the litigation." Id. at 435, 103 S.Ct. 1933. "Where a plaintiff has obtained excellent results, his attorney should recover a fully compensatory fee." Id. A plaintiff may obtain excellent results without receiving all the relief requested. Id. at 435 n. 11, 103 S.Ct. 1933.

Here, the district court found that Plaintiffs had achieved an "excellent result" and awarded a fully compensatory fee. The court stated that this action "represents eight years of sustained legal effort . . . to bring about a common good," namely the improvement of the disability determination system in Oregon. That "mission," the court found, "was accomplished."

Thus, the district court found that Plaintiffs had achieved the goal of their class action and then went on to compensate their lawyers fully. It is clear that the court considered Plaintiffs' degree of success; and its finding that Plaintiffs "accomplished" their "mission" is the functional equivalent of a finding that they achieved an "excellent result." The district court did not abuse its discretion in refusing to reduce Plaintiffs' award of fees on this basis.

III. Award of Attorney Fees Based on a Uniform Rate of $132 Per Hour

Both the federal Defendant and Plaintiffs argue that the district court abused its discretion in basing the award of attorney fees on a uniform rate of $132 per hour.

A. Federal-Defendant Fees

The federal Defendant argues that the hourly rate was proper as to the hours that Plaintiffs' lawyers spent on claims against the state Defendants ("the state hours"), but not as to the hours that they spent on claims against the federal Defendant ("the federal hours"). With regard to the federal hours, Defendant argues that the district court improperly adjusted the attorney-fee award for inflation based on current, rather than historic, rates.

As noted, the EAJA set a maximum fee of $75 per hour, which was increased by amendment in 1996 to $125 per hour for cases commenced on or after March 29, 1996. District courts may adjust that fee to compensate for an increase in the cost of living. 28 U.S.C. § 2412(d)(2)(A). District courts have been determining the cost-of-living adjustment by multiplying the basic EAJA rate by the current consumer price index for urban consumers (CPI-U), and then dividing the product by the CPI-U in the month that the cap was imposed (October 1981 for pre-amendment cases, March 1996 for post-amendment cases). Ramon-Sepulveda v. INS, 863 F.2d 1458, 1463 (9th Cir. 1988). The district court did so in this case and arrived at a maximum inflation-adjusted fee of $132 per hour under the EAJA.

The federal Defendant argues that the court's hourly rate is too high. In arriving at the inflation-adjusted rate of $132 per hour, the district court used the CPI-U that was current at the time that it issued its order, that is, in May 1999. The court applied that CPI-U to all hours that Plaintiffs had claimed under the EAJA, regardless of when those hours were expended.

Defendant urges, however, that the court should have used the versions of the CPI-U that applied to the years in which the hours actually were expended. To illustrate: In determining the inflation-adjusted value of an hour that one of Plaintiffs' lawyers billed in 1993, the district court should have multiplied the $75 base rate by the CPI-U for 1993, rather than the 1999 CPI-U that the court used. To do otherwise, Defendant argues, would be to charge unauthorized prejudgment interest against the government, contrary to the rule set out in Library of Congress v. Shaw, 478 U.S. 310, 320-21, 106 S.Ct. 2957, 92 L.Ed.2d 250 (1986) (holding that prejudgment interest may not be charged against the government in the absence of an express authorization by Congress).

We agree. Enhancing the EAJA's base rate by the CPI-U that is current in the year when the fee is earned compensates for increases in the cost of living between the time that the EAJA was enacted and the time that the fee was earned. But using the CPI-U that is current when the judgment is entered does more; it adjusts the fee to account for increases in the cost of living between the time that the fee was earned and the time that the government pays the fee. Such an adjustment compensates a lawyer for a delay in payment and is the functional equivalent of prejudgment interest. See, e.g., Masonry Masters, Inc. v. Nelson, 105 F.3d 708, 711 (D.C. Cir. 1997) (so stating); Shaw, 478 U.S. at 322, 106 S.Ct. 2957 ("Interest and a delay factor share an identical function. They are designed to compensate for the belated receipt of money.").

Under Shaw, an award of prejudgment interest against the government is improper unless expressly authorized by Congress. Id. at 320-21, 106 S.Ct. 2957. In determining whether Congress expressly authorized prejudgment interest in the EAJA, we are mindful that the EAJA "amounts to a partial waiver of sovereign immunity. Any such waiver must be strictly construed in favor of the United States." Ardestani v. INS, 502 U.S. 129, 137, 112 S.Ct. 515, 116 L.Ed.2d 496 (1991).

Congress did not waive sovereign immunity from prejudgment interest when it enacted the EAJA. The statute's cost-of-living provision is silent on the subject of interest, simply providing for an upward adjustment if "the court determines that an increase in the cost of living . . . justifies a higher fee." 28 U.S.C. § 2412(d)(2)(A). Silence cannot be interpreted as an express waiver of sovereign immunity for interest. In so holding, we join the other circuit courts that have considered the relationship between the EAJA's cost-of-living provision and the principle of sovereign immunity from prejudgment interest described in Shaw. Kerin, 218 F.3d at 194; Masonry Masters, 105 F.3d at 711; Marcus v. Shalala, 17 F.3d 1033, 1040 (7th Cir. 1994); Perales v. Casillas, 950 F.2d 1066, 1076-77 (5th Cir. 1992); Chiu v. United States, 948 F.2d 711, 720 (Fed. Cir. 1991).

In three published opinions, this court used the most recent CPI-U to determine a cost-of-living increase under the EAJA. Russell v. Sullivan, 930 F.2d 1443, 1446 (9th Cir. 1991); Animal Lovers Volunteer Ass'n v. Carlucci, 867 F.2d 1224, 1227 n. 2 (9th Cir. 1989); Ramon-Sepulveda, 863 F.2d at 1463 n. 4. However, those opinions neither discussed the question of which CPI-U should be used nor considered the issue of sovereign immunity from prejudgment interest. Rather, they simply used the current CPI-U without explanation. "Such unstated assumptions on non-litigated issues are not precedential holdings binding future decisions." Sakamoto v. Duty Free Shoppers, Ltd., 764 F.2d 1285, 1288 (9th Cir. 1985); see also Estate of Magnin v. Commissioner, 184 F.3d 1074, 1077 (9th Cir. 1999) ("When a case assumes a point without discussion, the case does not bind future panels.").

In sum, although the district court followed the "unstated assumptions" in our earlier cases, it made an error of law in adjusting Plaintiffs' EAJA fees according to the current version of the CPI-U. On remand, the court should calculate the cost-of-living adjustment according to the CPI-U for the year in which the fees were earned. See Kerin, 218 F.3d at 194; Masonry Masters, 105 F.3d at 711; Marcus, 17 F.3d at 1040.

B. State-Defendant Fees

In their cross-appeal, Plaintiffs argue that the district court abused its discretion in awarding fees for the state hours based on a rate of $132 per hour. As noted, the "applicable legal standards" for the state hours are the standards for awards under 42 U.S.C. § 1988. Under that statute, fees are based on the "prevailing market rates in the relevant community, regardless of whether plaintiff is represented by private or nonprofit counsel." Blum, 465 U.S. at 895, 104 S.Ct. 1541.

Plaintiffs' lawyers claimed market rates of between $150 and $350 per hour. They submitted affidavits and other documents to support their claim that those rates "are in line with those prevailing in the community for similar services by lawyers of reasonably comparable skill, experience and reputation." Id. at 895 n. 11, 104 S.Ct. 1541. That evidence stands essentially unrebutted in this record.

Nevertheless, the district court awarded fees based on an hourly rate of $132 per hour for all hours, including the state hours. The district court did not find that $132 per hour was the market rate for Plaintiffs' lawyers, from the most senior to the most junior. Rather, the court explained that rate on the grounds that (1) this was a "joint effort," (2) an unspecified part of the claim was restricted to $132 per hour under the EAJA, and (3) some of the hours that Plaintiffs claimed were poorly documented or unnecessary. But none of those factors pertains to the "market rate," which is what a court must use to determine a fee under § 1988.

We cannot determine from the district court's order whether it accepted Plaintiffs' evidence concerning the market rate or, if not, why not. By using the EAJA rate, instead of the standard method of determining fees under § 1988 for the state hours, the court awarded fees that appear on this record to be considerably below the market rate, at least for some of Plaintiffs' lawyers. Accordingly, we reverse and remand with instructions for the district court to award fees for the state hours according to the market rate.

That task is made more complicated by the fact that the district court has not made a finding about which hours are "state hours" and which are "federal hours." Without a finding on that point, we cannot determine how many hours should be compensated at the EAJA rate, and how many at the market rate under § 1988. On remand, the district court also should take evidence and make such a finding.

CONCLUSION

For the reasons stated, we AFFIRM the district court's order in part, REVERSE it in part, and REMAND for further proceedings consistent with this opinion. Each party is to bear its own costs on appeal.