opinion: Mr. Justice Stewart
  delivered the opinion of the Court.
  The question in this litigation concerns the constitutional validity of a legislative reapportionment plan devised by a three-judge Federal District Court for Mississippi’s Senate and House of Representatives. In Nos. 76-777 and 76-935, the appellants are the Mississippi voters who originally brought this class action in the District Court. They challenge the court’s entire Senate plan, and aspects of the House plan, as failing to meet the basic one-person, one-vote requirements of the Equal Protection Clause of the Fourteenth Amendment, and particularly the constitutional and equitable requirements of a court-ordered reapportionment plan. In No. 76-934 the appellant is the Government, an intervenor in the District Court. These appellants join in asserting that the District Court’s plan works an impermissible dilution, of Negro voting strength, and they challenge as well the District Court’s decree for its failure to order special elections in all legislative districts where new or significantly stronger Negro voting majorities were created by the District Court’s plan. In No. 76-933 the appellants are the state officers who were named as defendants in the District Court. These appellants assert that the District Court should have accorded greater deference to Mississippi’s historic policy of respecting county boundaries and thus should have established multimember legislative districts, and they further assert that the court erred in ordering any special elections at all.
  We do not reach all the complicated issues raised by the various appellants, because we have concluded that both the Senate and the House reapportionments ordered by the District Court fail to meet the most elemental requirement of the Equal Protection Clause in this area — that legislative districts be “as nearly of equal population as is practicable.” Reynolds v. Sims, 377 U. S. 533, 577; Chapman v. Meier, 420 U. S. 1.
  I
  The effort to reapportion the Mississippi Legislature in accordance with constitutional requirements has occupied the attention of the federal courts for 12 years. This painfully protracted process of litigation began in the wake of Reynolds v. Sims, supra, when the appellants in No. 76-777 challenged in the District Court for the Southern District of Mississippi, the extreme population variances of the legislative apportionment that had been enacted by the state legislature in 1962. The District Court invalidated that plan. Connor v. Johnson, 256 F. Supp. 962. After waiting for an ultimately unsuccessful attempt by the legislature to enact a constitutional reapportionment, the District Court then promulgated its own plan for the 1967 quadrennial elections, relying rather extensively on multimember districting in both legislative houses to achieve substantial population equality. Connor v. Johnson, 265 F. Supp. 492.
  In 1971, the state legislature enacted another apportionment; that legislation was held unconstitutional because the District Court could find no justification for the continuing substantial population variances among the various legislative districts. Connor v. Johnson, 330 F. Supp. 506. The court consequently formulated its own plan to govern the 1971 elections, continuing to rely extensively on multimember districts, and failing altogether to formulate a final plan with respect to the State’s three largest counties — Hinds, Harrison, and Jackson. Those counties instead were given interim multimember representation. In an interlocutory appeal from that order, this Court pointed out that single-member districts are preferable to large multimember districts in court-ordered reapportionment plans, and accordingly stayed the judgment of the District Court and instructed it “absent insurmountable difficulties, to devise and put into effect a single-member district plan for Hinds County.” Connor v. Johnson, 402 U. S. 690, 692. The District Court found itself confronted by insurmountable. difficulties, however, and did not divide Hinds County into single-member districts before the 1971 election. Connor v. Johnson, 330 F. Supp. 521.
  On direct appeal, after the 1971 elections had taken place pursuant to the District Court’s plan, this Court declined to consider the prospective validity of the 1971 plan in the continued absence of a final plan redistricting Hinds, Harrison, and Jackson Counties. Connor, v. Williams, 404 U. S. 549. Relying on the District Court’s stated intention to appoint a Special Master in January 1972 to consider the subdivision of those counties into single-member districts, we vacated the judgment and remanded with directions to the District Court that “[s]uch proceedings should go forward and be promptly concluded.” Id., at 551.
  No Special Master was appointed. In anticipation of the 1975 elections, however, the Mississippi Legislature in April 1973 enacted a new apportionment. A hearing was not held on the plaintiffs’ prompt objections to that legislation until February 1975. Before the District Court reached a decision, however, the Mississippi Legislature enacted yet another apportionment almost identical to the 1971 court-ordered plan, but permanently adopting multimember districts for Hinds, Harrison, and Jackson Counties. The District Court ordered the filing of a new complaint addressing the 1975 legislation, and concluded that it was constitutional. Connor v. Waller, 396 F. Supp. 1308. We reversed, holding that the legislative apportionment could not be effective as law until it had been submitted and had received clearance under § 5 of the Voting Rights Act of 1965, as amended, 42 U. S. C. § 1973c, and that the District Court had accordingly erred in considering its constitutional validity. Connor v. Waller, 421 U. S. 656.
  In compliance with § 5 of the Voting Rights Act, Mississippi then submitted the 1975 legislation to the Attorney General of the United States. When he objected to the legislation, the District Court proceeded to formulate another temporary reapportionment plan using multimember districts for the conduct of the 1975 elections. When the District Court delayed consideration of a permanent plan for the 1979 elections, this Court allowed the filing of a petition for a writ of mandamus to compel the District Court to enter a final judgment embodying a permanent reapportionment plan for the Mississippi Legislature. Connor v. Coleman, 425 U. S. 675. The District Court thereupon held hearings and entered a judgment adopting a final plan. See 419 F. Supp. 1072, 419 F. Supp. 1089, 422 F. Supp. 1014. We noted probable jurisdiction of these appeals challenging that judgment. 429 U. S. 1010 and 1060.
  II
  In approaching the task of devising a reapportionment plan for the 122-member House and 52-member Senate, the District Court announced certain guidelines to structure its analysis, drawn from previous cases in this court and other courts and from Mississippi policy. Population variances were to be as “near de minimis as possible”; districts were to be reasonably contiguous and compact; Negro voting strength would not be minimized or canceled; and every effort would be made to maintain the integrity of county lines. The plaintiffs do not really challenge the criteria enunciated by the District Court, but rather argue that the court failed to abide by its criteria in putting together the reapportionment plans. The defendants, as cross-appellants, argue by contrast that the District Court went too far, and that the Mississippi policy of respecting county lines required the court to continue the utilization of multimember districts.
  This litigation is a classic example of the proposition that “ 'the federal courts are often going to be faced with hard remedial problems' in minimizing friction between their remedies and legitimate state policies.” Taylor v. McKeithen, 407 U. S. 191, 194, quoting Sixty-seventh Minnesota State Senate v. Beens, 406 U. S. 187, 204 (dissenting opinion). The essential question here is whether the District Court properly exercised its equitable discretion in reconciling the requirements of the Constitution with the goals of state political policy.
  Although every state reapportionment plan is fraught with its own peculiar factual difficulties, it can hardly be said that this Court has given no guidance of general applicability to a court confronted with the need to devise a legislative reapportionment plan when the state legislature has failed. We have made clear that in two important respects a court will be held to stricter standards in accomplishing its task than will a state legislature: ''[U]nless there are persuasive justifications, a court-ordered reapportionment plan of a state legislature must avoid use of multimember districts, and, as well, must ordinarily achieve the goal of population equality with little more than de minimis variation.” Chapman v. Meier, 420 U. S., at 26-27.
  These high standards reflect the unusual position of federal courts as draftsmen of reapportionment plans. We have repeatedly emphasized that “legislative reapportionment is primarily a matter for legislative consideration and determination,” Reynolds v. Sims, 377 U. S., at 586, for a state legislature is the institution that is by far the best situated to identify and then reconcile traditional state policies within the constitutionally mandated framework of substantial population equality. The federal courts by contrast possess no distinctive mandate to compromise sometimes conflicting state apportionment policies in the people’s name. In the wake of a legislature’s failure constitutionally to reconcile these conflicting state and federal goals, however, a federal court is left with the unwelcome obligation of performing in the legislature’s stead, while lacking the political authoritativeness that the legislature can bring to the task. In such circumstances, the court’s task is inevitably an exposed and sensitive one that must be accomplished circumspectly, and in a manner “free from any taint of arbitrariness or discrimination.” Roman v. Sincock, 377 U. S. 695, 710.
  A
  Because the practice of multimember districting can contribute to voter confusion, make legislative representatives more remote from their constituents, and tend to submerge electoral minorities and overrepresent electoral majorities, this Court has concluded that single-member districts are to be preferred in court-ordered legislative reapportionment plans unless the court can articulate a “singular combination of unique factors” that justifies a different result. Mahan v. Howell, 410 U. S. 315, 333; Chapman v. Meier, supra, at 21; East Carroll Parish School Board v. Marshall, 424 U. S. 636, 639. In its final plan, and over the defendants’ objection, the District Court in the present case accordingly abandoned — albeit reluctantly — its previous adherence to multimember districting. The defendants’ unallayed reliance on Mississippi’s historic policy against fragmenting counties is insufficient to overcome the strong preference for single-member districting that this Court originally announced in this very litigation. Connor v. Johnson, 402 U. S., at 692; Connor v. Williams, 404 U. S., at 551.
  B
  The Equal Protection Clause requires that legislative districts be of nearly equal population, so that each person's vote may be given equal weight in the election of representatives. Reynolds v. Sims, supra. It was recognition of that fundamental tenet that motivated judicial involvement in the first place in what had. been called the “political thicket” of legislative apportionment. Baker v. Carr, 369 U. S. 186. The District Court's plan nevertheless departs from that norm in deference to Mississippi's historic respect for the integrity of county boundaries in conjunction with legislative districts. The result, as the District Court itself recognized, was “greater variances in population percentages in some instances than ordinarily would have been preferred.” 419 F. Supp., at 1076.
  Given the 1970 Mississippi population of 2,216,912 to be apportioned among 52 Senate districts, the population norm for a Senate seat if absolute population equality were to be achieved would be 42,633. As computed by the District Court, the Senate plan contains a maximum deviation from population equality of 16.5%, with the largest variances occurring in District 6 (8.2% above the norm) and in District 38 (8.3% below the norm). Fourteen of the court’s 52 Senate districts have variances from population equality of over 5%, plus or minus, and four of those have variances of 8% or more, plus or minus. In the House plan, with 122 seats, and a population norm of 18,171, there is a maximum deviation of 19.3%, with the largest variances occurring in District 5 (9.4% over the norm) and District 47 (9.9% below the norm). Forty-eight districts vary more than 5% either way, and 11 of those districts vary more than 8% either way.
  Such substantial deviations from population equality simply cannot be tolerated in a court-ordered plan, in the absence of some compelling justification:
  “With a court plan, any deviation from approximate population equality must be supported by enunciation of historically significant state policy or unique features.
  “. . . [A] court-ordered reapportionment plan of a state legislature . . . must ordinarily achieve the goal of population equality with little more than de minimis variation. Where important and significant state considerations rationally mandate departure from these standards, it is the reapportioning court’s responsibility to articulate precisely why a plan of single-member districts with minimal population variance cannot be adopted.” Chapman v. Meier, 420 U. S., at 26-27 (footnote omitted).
  The maximum population deviations of 16.5% in the Senate districts and 19.3% in the House districts can hardly be characterized as de minimis; they substantially exceed the “under-10%” deviations the Court has previously considered to be of prima facie constitutional validity only in the context of legislatively enacted apportionments. See Gaffney v. Cummings, 412 U. S. 735 (7.83%- maximum deviation from the population norm); White v. Regester, 412 U. S. 755 (9.9% maximum deviation from the population norm). Hence even a legislatively crafted apportionment with deviations of this magnitude could be justified only if it were “based on legitimate considerations incident to the effectuation of a rational state policy.” Reynolds v. Sims, 377 U. S., at 579, quoted in Mahan v. Howell, 410 U. S., at 325.
  As justification for both the Senate and House plans, the District Court pointed to a fairly consistent state policy of maintaining the borders of its 82 counties when allotting seats in the legislature, and to the fact that this policy is rationalized in part by the lack of legislative powers entrusted to the counties, whose legislative needs must instead be met by reliance on private bills introduced by members of the state legislature. But the District Court itself recognized at an earlier stage in this litigation that the policy against breaking county boundary lines is virtually impossible of accomplishment in a State where population is unevenly distributed among 82 counties, from which 52 Senators and 122 House members are to be elected. Only 11 of 82 counties have enough people to elect a Senator, and only 44 counties have enough people to elect a Representative. Connor v. Johnson, 330 F. Supp., at 509.
  The policy of maintaining the inviolability of county lines in such circumstances, if strictly adhered to, must inevitably collide with the basic equal protection standard of one person, one vote. Indeed, Mississippi’s insistent adherence to that policy resulted in the invalidation of three successive legislative apportionments as constitutionally impermissible. See Connor v. Johnson, 256 F. Supp. 962; Connor v. Johnson, 265 F. Supp. 492; Connor v. Johnson, 330 F. Supp. 506.
  Recognition that a State may properly seek to protect the integrity of political subdivisions or historical boundary lines permits no more than “minor deviations” from the basic requirement that legislative districts must be “as nearly of equal population as is practicable.” Roman v. Sincock, 377 U. S., at 710; Reynolds v. Sims, supra, at 577. The question is one of degree. In Chapman v. Meier, however, it was established that the latitude in court-ordered plans for departure from the Reynolds standards in order to maintain county lines is considerably narrower than that accorded apportionments devised by state legislatures, and that the burden of articulating special reasons for following such a policy in the face of substantial population inequalities is correspondingly higher. The District Court failed here to identify any such “unique features” of the Mississippi political structure as would permit a judicial protection of county boundaries in the teeth of the judicial duty to “achieve the goal of population equality with little more than de minimis variation.” Chapman v. Meier, supra, at 26-27.
  Under the less stringent standards governing legislatively adopted apportionments, the goal of maintaining political subdivisions as districts sufficed to justify a 16.4% population deviation in the plan for the Virginia House of Delegates. Mahan v. Howell, 410 U. S. 315. But in Mahan, there was uncontradicted evidence that the legislature’s plan “ 'produces the minimum deviation above and below the norm, keeping intact political boundaries.’ ” Id., at 326. By contrast, the plaintiffs in this case submitted to the District Court an alternative Senate plan that served the state policy against fragmenting county boundaries better than did the plan the court ultimately adopted, and also came closer to achieving districts that are “as nearly of equal population as is practicable.” Reynolds v. Sims, supra, at 577. The 19 county boundaries cut by the court plan would have been reduced to 15 in the so-called “Modified Henderson Plan” submitted by the plaintiffs; the maximum population deviation in any district would have been reduced from 16.5% to 13.66%, and the number of districts deviating by more than 5% from the population norm, plus or minus, would have been reduced from 15 to 9. As in Chapman, “our reference to the [Henderson] plan is to show that the factors cited by the District Court cannot be viewed as controlling and persuasive when other, less statistically offensive, plans already devised are feasible.” 420 U. S., at 26. See also Kilgarlin v. Hill, 386 U. S. 120, 124; Swann v. Adams, 385 U. S. 440, 445-446.
  In the absence of a convincing justification for its continued adherence to a plan that even in state policy terms is less efficacious than another plan actually proposed, there can be no alternative but to set aside the District Court’s decree for its failure to embody the equitable discretion necessary to effectuate the established standards of the Equal Protection Clause.
  Ill
  Since the District Court’s legislative reapportionment decree is invalid under the elementary standards of Reynolds v. Sims, we do not reach the more particularized challenges to certain aspects of that reapportionment plan made by the plaintiffs — challenges based upon claims that the plan’s apportionment of some districts impermissibly dilutes Negro voting strength. Swann v. Adams, supra, at 446-447. But since the 1979 elections are on the horizon and a constitutionally permissible legislative reapportionment plan for the State of Mississippi has yet to be drawn, it is appropriate to give some further guidance to the District Court with these challenges in mind. Cf. Chapman v. Meier, 420 U. S., at 26.
  To support their claim of impermissible racial dilution, the plaintiffs point to unexplained departures from the neutral guidelines the District Court adopted to govern its formulation of a reapportionment plan — departures which have the apparent effect of scattering Negro voting concentrations among a number of white majority districts. They point in particular to the District Court’s failure adequately to explain its adoption of irregularly shaped districts when alternative plans exhibiting contiguity, compactness, and lower or acceptable population variances were at hand. The plaintiffs have referred us to two types of situations in which the District Court’s decree fails to meet its own goal that legislative districts be reasonably contiguous and compact: in its subdivisions of large counties whose population entitles them to elect several legislative representatives to both houses, and in its aggregations of smaller counties to put together enough people to elect one legislator.
  Hinds County exemplifies the large county problem. It is the site of the State’s largest city, Jackson, and is the most populous Mississippi county, with a total of 214,973 residents, 84,064 of whom are Negroes. As are all Mississippi counties, Hinds is divided into five supervisory districts or “beats”; each beat elects one supervisor to sit on the Board of Supervisors, which is charged with executive and judicial local government responsibilities. The Board of Supervisors reapportioned itself in 1969, creating five oddly shaped beats that extend from the far corners of the county in long corridors that fragment the city of Jackson, where much of the Negro population is concentrated. See Kirksey v. Board of Supervisors of Hinds County, 402 F. Supp. 658 (SD Miss.), aff’d, 528 F. 2d 536 (CA5), awaiting decision after rehearing en banc. The irregular shapes of the beats were assertedly justified as necessary to achieve equalization of road mileage, bridges, and land area among the districts, so as to equalize the primary responsibilities of the supervisors — maintenance of the roads and bridges. Whatever may be the validity of those justifications for a Hinds County Board of Supervisors’ apportionment first adopted in 1969, they are irrelevant to the problem of apportioning state senate seats, whose holders will presumably concern themselves with something other than maintaining roads and bridges. The District Court nevertheless concluded that each Hinds County beat should elect one Senator.
  The District Court did not explain its preference for the Hinds County Board of Supervisors’ plan, although it did note generally that “we have had to take the Counties, Beats, and [voting] precincts as they actually are.” There is, however, no longstanding state policy mandating separate representation of individual beats in the legislature. And there is no practical barrier that requires apportioning a large county on the basis of beat lines; Mississippi’s 410 beats are in turn divided into 2,094 voting precincts, each of which is sufficiently small as the basic voting unit to allow considerable flexibility in putting together legislative districts. On this record, neither custom nor practical necessity can thus be said to justify reliance for state senatorial districting purposes upon the beats adopted by the Hinds County Board of Supervisors to govern their own election.
  The District Court’s treatment of Jefferson and Claiborne Counties illustrates a departure from its own announced standards in aggregating small counties to form a single-member legislative district. Jefferson and Claiborne Counties are contiguous counties on the western border of Mississippi. Claiborne has a total population of 10,086, of whom 7,522 are Negroes. Jefferson has a total population of 9,295 of whom 6,996 are Negroes. The plaintiffs suggested combining these two counties with Copiah County to make a compact Senate district with a 55% Negro voting-age population. Instead, and without explanation, the District Court combined Claiborne County with Lincoln County and with Beat 3 of Copiah County to make a white majority senatorial district; Jefferson County was combined with Beats 1, 2, 4, and 5 of Adams County to make an irregularly shaped senatorial district with a slight Negro voting-age majority. Compared to the plaintiffs’ proposals, the District Court’s senatorial districts are less compact, and in addition require the fragmentation of two counties while the plaintiffs’ proposal would have fragmented none.
  Such unexplained departures from the results that might have been expected to flow from the District Court’s own neutral guidelines can lead, as they did here, to a charge that the departures are explicable only in terms of a purpose to minimize the voting strength of a minority group. The District Court could have avoided this charge by more carefully abiding by its stated intent of adopting reasonably contiguous and compact districts, and by fully explaining any departures from that goal.
  Twelve years have passed since this litigation began, but ■ there is still no constitutionally permissible apportionment plan for the Mississippi Legislature. It is therefore imperative for the District Court, in drawing up a new plan, to make every effort not only to comply with established constitutional standards, but also to allay suspicions and avoid the creation of concerns that might lead to new constitutional challenges, In view of the serious questions raised concerning the purpose and effect of the present decree’s unusually shaped legislative districts in areas with concentrations of Negro population, the District Court on remand should either draw legislative districts that are reasonably contiguous and compact, so as to put to rest suspicions that Negro voting strength is being impermissibly diluted, or explain precisely why in a particular instance that goal cannot be accomplished.
  The task facing the District Court on remand must be approached not only with great care, but with a compelling awareness of the need for its expeditious accomplishment, so that the citizens of Mississippi at long last will be enabled to elect a legislature that properly represents them.
  Reversed and remanded.
  Mr. Justice Rehnquist took no part in the consideration or decision of these cases.
  These appellants also challenge the District Court’s failure to award them reasonable attorneys’ fees, as authorized by § 402 of the 1975 amendments to the Voting Rights Act of 1965, 42 U. S. C. § 1973l (e) (1970 ed., Supp. V), and the recent Civil Rights Attorney’s Fees Awards Act of 1976, 90 Stat. 2641, 42 U. S. C. § 1988 (1976 ed.). Because we reverse and remand this cause for further proceedings, we do not resolve this problem, but simply instruct the District Court to make a determination of this question at an appropriate time in the proceedings on remand.
  The appellants in Nos. 76-777, 76-934, and 76-935 will sometimes hereinafter be referred to as the plaintiffs.
  Under the 1962 regime a majority of the House of Representatives could have been elected by some 40% of the State’s voters; a majority of the Senate could have been elected by less than 38% of them. Connor v. Johnson, 256 F. Supp., at 976-977.
  Thirty-four of the 52 House districts and 10 of the 36 Senate districts were multimember districts under this court plan.
  Most of the House districts and almost half of the Senate districts were constituted as multimember districts under this plan. Thus 52 Senators were to be elected from 33 senatorial districts, and 122 Members of the House of Representatives were to be elected from 46 House districts. Connor v. Johnson, 330 F. Supp., at 509-516.
  This Court was advised at that time that acceptable single-member district plans had been worked out for Hinds County, but not for Harrison or Jackson County. Connor v. Johnson, 402 U. S. 690.
  The 1975 legislative plan contained 14 multimember districts for the Senate, and 24 multimember districts and 34 floterial districts and subdistricts for the House. (Floterial districts are a form of multimember districting in which one or more legislators are elected from subdistricts and one or more legislators are elected districtwide.) Connor v. Waller, 396 F. Supp., at 1324-1325, 1333-1339.
  On June 10, 1975, the Attorney General objected to the 1975 Acts reapportioning the House and Senate on the ground that Mississippi had failed to show that the legislation did not have the purpose and would not have the effect of denying or abridging the right to vote on account of race. The United States was subsequently permitted to intervene in the District Court as a party plaintiff. Connor v. Finch, 419 F. Supp. 1089, 1090-1091.
  This Court directed the District Court promptly to bring this case to trial, and not to await this Court’s decisions in other cases raising reapportionment questions. On the assumption that the District Court would hold a hearing within 30 days of the entry of this Court’s order, we deferred consideration of the petition for writ of mandamus until June 17, 1976.
  The District Court postulated two specific guidelines on county boundary integrity:
  “1. If a county has more than enough population for the election of a Representative or Senator, then there shall be one complete district within that county, thus at least one Senator or Representative will be chosen solely by that county. In practical effect this will largely preserve the integrity of county boundaries and conform, to a degree, with the state policy on that subject, Mahan v. Howell [410 U. S. 315],
  “2. Except where two or more districts may properly be set up within the same county as authorized by Mississippi Constitution, Section 254, no county will be split into more than two segments.” (Emphasis in original.) Connor v. Finch, 419 F. Supp. 1072, 1076.
  See also Chapman v. Meier, 420 U. S. 1, 27; Connor v. Williams, 404 U. S. 549, 552 n. 4; Burns v. Richardson, 384 U. S. 73, 85.
  Miss. Const., Art. 13, § 255.
  In gauging the total population deviations from the House and Senate norms, we accept the District Court’s calculation of district populations and population deviations. As is not unusual in cases such as this, there is considerable controversy among the parties as to what the proper population figures are. The census is itself at best an approximate estimate of a State’s population at a frozen moment in time. Because it is taken by census tract rather than along supervisory district or voting precinct lines, relevant population figures for these political districts have to be extrapolated. That process is complicated by the recognition that major shifts in population and in voting precinct lines have occurred since the 1970 census, and by the fact that proportionally more Negroes than whites are ineligible to vote because of age.
  We need not “enter this imbroglio of mathematical manipulation,” but instead “confine our consideration to the figures actually found by the court.” Mahan v. Howell, 410 U. S. 315, 319 n. 6. See also Burns v. Richardson, supra, at 91-93. On remand, however, to avoid the substantial confusion that characterizes the record now before us, the District Court should explain the genesis of the population figures on which it relies.
  We note that the appellants in No. 76-935 assert that simple mathematical error resulted in understating the population variance in Senate District 29. According to their figures, that district has a variance of 9.96%, resulting in a maximum deviation in the court’s Senate plan of 18.29%.
  Miss. Const., Art. 13, § 254.
  The District Court originally calculated the total variance at 18.5%, but its December 21, 1976, order, amending its previous judgment, increased the variance in District 47 from —9.1% to —9.9%.
  The Court refused to assume in Chapman v. Meier that even a 5.95% deviation from the norm would necessarily satisfy the high standards required of court-ordered plans.
  As justification for the high population deviations in the House plan, the District Court also “emphasize [d] that the exceedingly low 1% population norm of 181 persons has made our task ... far more difficult” — i. e., the small population of the House districts means that, any underinclusion or overinclusion of 181 persons in a district results in an incremental 1% deviation from the population norm for that district. 419 F. Supp., at 1112. The 1% population norm in the sparsely populated State of North Dakota was 121, but the Court did not consider that a “legitimate basis for a departure from the goal of equality” in Chapman v. Meier, 420 U. S., at 24. Instead we recognized that “each individual vote may be more important to the result of an election” in such circumstances, and concluded that “particular emphasis should be placed on establishing districts with as exact population equality as possible.” Id., at 25.
  The appellants in No. 76-935 challenged the Senate reapportionment as a whole under Reynolds v. Sims. They did not make a blanket challenge to the entire House plan under the Reynolds v. Sims doctrine, since they viewed it as “go[ing] a long way toward alleviating the dilution of black voting strength present in the 1971 and 1975 . . . court-ordered House plans.” They did, however, challenge several districts in the House plan as excessively malapportioned (arguing, for example, that the plan created a total deviation of 18.2% for four House districts in Washington and Issaquena Counties), and all of the plaintiffs supported their claims of fragmentation of Negro voting strength by pointing to significant deviations from the House population norm.
  In the context of a court-ordered plan that results in the sort of systemic violation revealed by the figures in this record, it is hardly appropriate to confine our scrutiny to particularly egregious, but localized examples of violations specifically relied on by the parties. And even if the constitutional validity of the entire court-ordered House plan could not appropriately be viewed as an issue implicitly raised by the parties, this Court has the authority and the duty in exceptional circumstances to notice federal-court errors to which no exception has been taken, when they “seriously affect the fairness, integrity or public reputation of judicial proceedings.” United States v. Atkinson, 297 U. S. 157, 160, quoted in Silber v. United States, 370 U. S. 717, 718. See also Blonder-Tongue Laboratories v. University Foundation, 402 U. S. 313, 320 n. 6; Sibbach v. Wilson, 312 U. S. 1, 16; R. Stern & E. Gressman, Supreme Court Practice §6.37 (4th ed. 1969).
  The plaintiffs also argue that special elections should have been ordered in a number of House and Senate districts to remedy the serious deficiencies in the 1975 court-ordered plan under which the present state legislature was elected. These arguments, too, become moot in view of the invalidity of the entire reapportionment decree now before us.
  The plaintiffs assert that the reapportionment decree, if found to dilute Negro voting strength, is unconstitutional under the Fourteenth and Fifteenth Amendments. Our limited comments here, however, are addressed only to the question of the District Court’s appropriate exercise of its discretion in remedying the Mississippi Legislature’s failure to enact a valid apportionment under the equal protection standards established by Reynolds v. Sims. Cf. Ashwander v. TVA, 297 U. S. 288, 347 (Brandeis, J., concurring).
  See, e. g., White v. Regester, 412 U. S. 755; Whitcomb v. Chavis, 403 U. S. 124; Abate v. Mundt, 403 U. S. 182, 184 n. 2; Burns v. Richardson, 384 U. S., at 88-89; Fortson v. Dorsey, 379 U. S. 433, 439.
  The textual examples are meant to be illustrative rather than an exhaustive- catalogue of possible deficiencies in the District Court’s plan. Similar criticisms could possibly be made of the districting contours in a number of other counties.
  The validity of these justifications for apportionment of the supervisor beats is currently under attack in Kirksey v. Board of Supervisors of Hinds County, pending in the Court of Appeals for the Fifth Circuit after reargument en banc. Our discussion of the Hinds County Senate districting problem is not to be understood as pretermitting that court’s consideration of the county supervisor districting issue raised in the Kirksey litigation.
  Unlike counties with “boundaries . . . fixed by statute for generations,” beats are not units of state government, and their boundaries are frequently changed by the Boards of Supervisors. According to the District Court: “Beat lines generally follow governmental land lines as laid down by section, township, and range — -in other words invisible to all, and unknown to most. It is a rare individual who knows where a beat line is at any given point . . . .” Connor v. Johnson, 330 F. Supp., at 518.
  The District Court did take a substantial step forward in its final decree by eliminating multimember districts. In setting aside this decree we do not mean to obscure the significance of that advance. Although the court’s order to hold special elections in two districts to make more immediately available the fruits of its decree cannot be affirmed in the face of our judgment today that vacates the entire decree, the District Court will retain the power to order such special elections on remand as the circumstances may require or permit.
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