delivered the opinion of the Court.
The question presented by this appeal is whether an apportionment plan for congressional districts satisfies Art. I, §2, of the Constitution without need for further justification if the population of the largest district is less than one percent greater than the population of the smallest district. A three-judge District Court declared New Jersey’s 1982 reapportionment plan unconstitutional on the authority of Kirkpatrick v. Preisler, 394 U. S. 526 (1969), and White v. Weiser, 412 U. S. 783 (1973), because the population deviations among districts, although small, were not the result of a good-faith effort to achieve population equality. We affirm.
I
After the results of the 1980 decennial census had been tabulated, the Clerk of the United States House of Representatives notified the Governor of New Jersey that the number of Representatives to which the State was entitled had decreased from 15 to 14. Accordingly, the New Jersey Legislature was required to reapportion the State’s congressional districts. The State’s 199th Legislature passed two reapportionment bills. One was vetoed by the Governor, and the second, although signed into law, occasioned significant dissatisfaction among those who felt it diluted minority voting strength in the city of Newark. See App. 83-84, 86-90. In response, the 200th Legislature returned to the problem of apportioning congressional districts when it convened in January 1982, and it swiftly passed a bill (S-711) introduced by Senator Feldman, President pro tem of the State Senate, *728which created the apportionment plan at issue in this case. The bill was signed by the Governor on January 19, 1982, becoming Pub. L. 1982, ch. 1 (hereinafter Feldman Plan). A map of the resulting apportionment is appended infra.
Like every plan considered by the legislature, the Feldman Plan contained 14 districts, with an average population per district (as determined by the 1980 census) of 526,059.1 Each district did not have the same population. On the average, each district differed from the “ideal” figure by 0.1384%, or about 726 people. The largest district, the Fourth District, which includes Trenton, had a population of 527,472, and the smallest, the Sixth District, embracing most of Middlesex County, a population' of 523,798. The difference between them was 3,674 people, or 0.6984% of the average district. The populations of the other districts also varied. The Ninth District, including most of Bergen County, in the northeastern corner of the State, had a population of 527,349, while the population of the Third District, along the Atlantic shore, was only 524,825. App. 124.
The legislature had before it other plans with appreciably smaller population deviations between the largest and smallest districts. The one receiving the most attention in the District Court was designed by Dr. Ernest Reock, Jr., a political science professor at Rutgers University and Director of the Bureau of Government Research. A version of the Reock *729Plan introduced in the 200th Legislature by Assemblyman Hardwick had a maximum population difference of 2,375, or 0.4514% of the average figure. Id., at 133.
Almost immediately after the Feldman Plan became law, a group of individuals with varying interests, including all incumbent Republican Members of Congress from New Jersey, sought a declaration that the apportionment plan violated Art. I, §2, of the Constitution2 and an injunction against proceeding with the primary election for United States Representatives under the plan. A three-judge District Court was convened pursuant to 28 U. S. C. § 2284(a). The District Court held a hearing on February 26, 1982, at which the parties submitted a number of depositions and affidavits, moved for summary judgment, and waived their right to introduce further evidence in the event the motions for summary judgment were denied.
Shortly thereafter, the District Court issued an opinion and order declaring the Feldman Plan unconstitutional. Denying the motions for summary judgment and resolving the case on the record as a whole, the District Court held that the population variances in the Feldman Plan were not “unavoidable despite a good-faith effort to achieve absolute equality,” see Kirkpatrick, supra, at 531. The court rejected appellants’ argument that a deviation lower than the statistical imprecision of the decennial census was “the functional equivalent of mathematical equality.” Daggett v. Kimmelman, 535 F. Supp. 978, 982-983 (NJ 1982). It also held that appellants had failed to show that the population variances were justified by the legislature’s purported goals of preserving minor*730ity voting strength and anticipating shifts in population. Ibid. The District Court enjoined appellants from conducting primary or general elections under the Feldman Plan, but that order was stayed pending appeal to this Court, 455 U. S. 1303 (1982) (Brennan, J., in chambers), and we noted probable jurisdiction, 457 U. S. 1131 (1982).
hH I — I
Article I, § 2, establishes a “high standard of justice and common sense” for the apportionment of congressional districts: “equal representation for equal numbers of people.” Wesberry v. Sanders, 376 U. S. 1, 18 (1964). Precise mathematical equality, however, may be impossible to achieve in an imperfect world; therefore the “equal representation” standard is enforced only to the extent of requiring that districts be apportioned to achieve population equality “as nearly as is practicable.” See id., at 7-8, 18. As we explained further in Kirkpatrick v. Preisler:
“[T]he ‘as nearly as practicable’ standard requires that the State make a good-faith effort to achieve precise mathematical equality. See Reynolds v. Sims, 377 U. S. 533, 577 (1964). Unless population variances among congressional districts are shown to have resulted despite such effort, the State must justify each variance, no matter how small.” 394 U. S., at 530-531.
Article I, §2, therefore, “permits only the limited population variances which are unavoidable despite a good-faith effort to achieve absolute equality, or for which justification is shown.” Id., at 531. Accord, White v. Weiser, 412 U. S., at 790.
Thus two basic questions shape litigation over population deviations in state legislation apportioning congressional districts. First, the court must consider whether the population differences among districts could have been reduced or eliminated altogether by a good-faith effort to draw districts of equal population. Parties challenging apportionment leg*731islation must bear the burden of proof on this issue, and if they fail to show that the differences could have been avoided the apportionment scheme must be upheld. If, however, the plaintiffs can establish that the population differences were not the result of a good-faith effort to achieve equality, the State must bear the burden of proving that each significant variance between districts was necessary to achieve some legitimate goal. Kirkpatrick, 394 U. S., at 532; cf. Swann v. Adams, 385 U. S. 440, 443-444 (1967).
r-H h-1
Appellants principal argument in this case is addressed to the first question described above. They contend that the Feldman Plan should be regarded per se as the product of a good-faith effort to achieve population equality because the maximum population deviation among districts is smaller than the predictable undercount in available census data.
A
Kirkpatrick squarely rejected a nearly identical argument. “The whole thrust of the ‘as nearly as practicable’ approach is inconsistent with adoption of fixed numerical standards which excuse population variances without regard to the circumstances of each particular case.” 394 U. S., at 530; see White v. Weiser, supra, at 790, n. 8, and 792-793. Adopting any standard other than population equality, using the best census data available, see 394 U. S., at 532, would subtly erode the Constitution’s ideal of equal representation. If state legislators knew that a certain de minimis level of population differences was acceptable, they would doubtless strive to achieve that level rather than equality.3 Id., at *732531. Furthermore, choosing a different standard would import a high degree of arbitrariness into the process of reviewing apportionment plans. Ibid. In this case, appellants argue that a maximum deviation of approximately 0.7% should be considered de minimis. If we accept that argument, how are we to regard deviations of 0.8%, 0.95%, 1%, or 1.1%?
Any standard, including absolute equality, involves a certain artificiality. As appellants point out, even the census data are not perfect, and the well-known restlessness of the American people means that population counts for particular localities are outdated long before they are completed. Yet problems with the data at hand apply equally to any population-based standard we could choose.4 As between two standards — equality or something less than equality — only the former reflects the aspirations of Art. I, § 2.
To accept the legitimacy of unjustified, though small population deviations in this case would mean to reject the basic premise of Kirkpatrick and Wesberry. We decline appellants’ invitation to go that far. The unusual rigor of their standard has been noted several times. Because of that rigor, we have required that absolute population equality be the paramount objective of apportionment only in the case of *733congressional districts, for which the command of Art. I, § 2, as regards the National Legislature outweighs the local interests that a State may deem relevant in apportioning districts for representatives to state and local legislatures, but we have not questioned the population equality standard for congressional districts. See, e. g., White v. Weiser, 412 U. S., at 793; White v. Regester, 412 U. S. 755, 763 (1973); Mahan v. Howell, 410 U. S. 315, 321-323 (1973). The principle of population equality for congressional districts has not proved unjust or socially or economically harmful in experience. Cf. Washington v. Dawson & Co., 264 U. S. 219, 237 (1924) (Brandeis, J., dissenting); B. Cardozo, The Nature of the Judicial Process 150 (1921). If anything, this standard should cause less difficulty now for state legislatures than it did when we adopted it in Wesberry. The rapid advances in computer technology and education during the last two decades make it relatively simple to draw contiguous districts of equal population and at the same time to further whatever secondary goals the State has.5 Finally, to abandon unnecessarily a clear and oft-confirmed constitutional interpretation would impair our authority in other cases, Florida Dept. of Health v. Florida Nursing Home Assn., 450 U. S. 147, 153-154 (1981) (Stevens, J., concurring); Pollock v. Farmers’ Loan & Trust Co., 157 U. S. 429, 652 (1895) (White, J., dissenting), would implicitly open the door to a plethora of requests that we reexamine other rules that some may consider *734burdensome, Cardozo, supra, at 149-150, and would prejudice those who have relied upon the rule of law in seeking an equipopulous congressional apportionment in New Jersey, see Florida Nursing Home Assn., supra, at 154 (Stevens, J., concurring). We thus reaffirm that there are no de minimis population variations, which could practicably be avoided, but which nonetheless meet the standard of Art. I, §2, without justification.6
*735B
The sole difference between appellants’ theory and the argument we rejected in Kirkpatrick is that appellants have proposed a de minimis line that gives the illusion of rationality and predictability: the “inevitable statistical imprecision of the census.” They argue: “Where, as here, the deviation from ideal district size is less than the known imprecision of the census figures, that variation is the functional equivalent of zero.” Brief for Appellants 18. There are two problems with this approach. First, appellants concentrate on the extent to which the census systematically undercounts actual population — a figure which is not known precisely and which, even if it were known, would not be relevant to this case. Second, the mere existence of statistical imprecision does not make small deviations among districts the functional equivalent of equality.
In the District Court and before this Court, appellants rely exclusively on an affidavit of Dr. James Trussell, a Princeton University demographer. See App. 97-104. Dr. Trussell’s carefully worded statement reviews various studies of the undercounts in the 1950, 1960, and 1970 decennial censuses, and it draws three important conclusions: (1) “the undercount in the 1980 census is likely to be above one percent”; (2) “all the evidence to date indicates that all places are not under-counted to the same extent, since the undercount rate has been shown to depend on race, sex, age, income, and education”; and (3) “[t]he distribution of the undercount in New Jersey is . . . unknown, and I see no reason to believe that it would be uniformly spread over all municipalities.” Id., at 103-104. Assuming for purposes of argument that each of *736these statements is correct, they do not support appellants’ argument.
In essence, appellants’ one-percent benchmark is little more than an attempt to present an attractive de minimis line with a patina of scientific authority. Neither Dr. Trussell’s statement nor any of appellants’ other evidence specifies a precise level for the undercount in New Jersey, and Dr. Trussell’s discussion of the census makes clear that it is impossible to develop reliable estimates of the undercount on anything but a nationwide scale. See id., at 98-101. His conclusion that the 1980 undercount is “likely to be above one percent” seems to be based on the undercounts in previous censuses and a guess as to how well new procedures adopted in 1980 to reduce the undercount would work. Therefore, if we accepted appellants’ theory that the national undercount level sets a limit on our ability to use census data to tell the difference between the populations of congressional districts, we might well be forced to set that level far above one percent when final analyses of the 1980 census are completed.7
As Dr. Trussell admits, id., at 103, the existence of a one-percent undercount would be irrelevant to population deviations among districts if the undercount were distributed evenly among districts. The undercount in the census affects the accuracy of the deviations between districts only to the extent that the undercount varies from district to district. For a one-percent undercount to explain a one-percent deviation between the census populations of two districts, the undercount in the smaller district would have to be approximately three times as large as the undercount in the larger *737district.8 It is highly unlikely, of course, that this condition holds true, especially since appellants have utterly failed to introduce evidence showing that the districts were designed to compensate for the probable undercount. Dr. Trussell’s affidavit states that the rate of undercounting may vary from municipality to municipality, but it does not discuss by how much it may vary, or to what extent those variations would be reflected at the district level, with many municipalities combined. Nor does the affidavit indicate that the factors associated with the rate of undercounting — race, sex, age, etc. — vary from district to district, or (more importantly) that the populations in the smaller districts reflect the relevant factors more than the populations in the larger districts.9 As Dr. Trussell admits, the distribution of the undercount in New Jersey is completely unknown. Only by bizarre coincidence could the systematic undercount in the *738census bear some statistical relationship to the districts drawn by the Feldman Plan.
The census may systematically undercount population, and the rate of undercounting may vary from place to place. Those facts, however, do not render meaningless the differences in population between congressional districts, as determined by uncorrected census counts. To the contrary, the census data provide the only reliable — albeit less than perfect — indication of the districts’ “real” relative population levels. Even if one cannot say with certainty that one district is larger than another merely because it has a higher census count, one can say with certainty that the district with a larger census count is more likely to be larger than the other district than it is to be smaller or the same size. That certainty is sufficient for decisionmaking. Cf. City of Newark v. Blumenthal, 457 F. Supp. 30, 34 (DC 1978). Furthermore, because the census count represents the “best population data available,” see Kirkpatrick, 394 U. S., at 528, it is the only basis for good-faith attempts to achieve population equality. Attempts to explain population deviations on the basis of flaws in census data must be supported with a precision not achieved here. See id., at 535.
C
Given that the census-based population deviations in the Feldman Plan reflect real differences among the districts, it is clear that they could have been avoided or significantly reduced with a good-faith effort to achieve population equality. For that reason alone, it would be inappropriate to accept the Feldman Plan as “functionally equivalent” to a plan with districts of equal population.
The District Court found that several other plans introduced in the 200th Legislature had smaller maximum deviations than the Feldman Plan. 535 F. Supp., at 982. Cf. White v. Weiser, 412 U. S., at 790, and n. 9. Appellants object that the alternative plans considered by the District Court were not comparable to the Feldman Plan because *739their political characters differed profoundly. See, e. g., App. 93-96 (affidavit of S. H. Woodson, Jr.) (arguing that alternative plans failed to protect the interests of black voters in the Trenton and Camden areas). We have never denied that apportionment is a political process, or that state legislatures could pursue legitimate secondary objectives as long as those objectives were consistent with a good-faith effort to achieve population equality at the same time. Nevertheless, the claim that political considerations require population differences among congressional districts belongs more properly to the second level of judicial inquiry in these cases, see infra, at 740-741, in which the State bears the burden of justifying the differences with particularity.
In any event, it was unnecessary for the District Court to rest its finding on the existence of alternative plans with radically different political effects. As in Kirkpatrick, “resort to the simple device of transferring entire political subdivisions of known population between contiguous districts would have produced districts much closer to numerical equality.” 394 U. S., at 532. Starting with the Feldman Plan itself and the census data available to the legislature at the time it was enacted, see App. 23-34, one can reduce the maximum population deviation of the plan merely by shifting a handful of municipalities from one district to another.10 *740See also Swann v. Adams, 385 U. S., at 445-446; n. 4, supra. Thus the District Court did not err in finding that the plaintiffs had met their burden of showing that the Feldman Plan did not come as nearly as practicable to population equality.
<1
By itself, the foregoing discussion does not establish that the Feldman Plan is unconstitutional. Rather, appellees’ success in proving that the Feldman Plan was not the product of a good-faith effort to achieve population equality means only that the burden shifted to the State to prove that the population deviations in its plan were necessary to achieve some legitimate state objective. White v. Weiser demonstrates that we are willing to defer to state legislative policies, so long as they are consistent with constitutional norms, even if they require small differences in the population of congressional districts. See 412 U. S., at 795-797; cf. Upham v. Seamon, 456 U. S. 87 (1982); Connor v. Finch, 431 U. S. 407, 414-415 (1977). Any number of consistently applied legislative policies might justify some variance, including, for instance, making districts compact, respecting municipal boundaries, preserving the cores of prior districts, and avoiding contests between incumbent Representatives. As long as the criteria are nondiscriminatory, see Gomillion v. Lightfoot, 364 U. S. 339 (1960), these are all legitimate objectives that on a proper showing could justify minor population deviations. See, e. g., West Virginia Civil Liberties Union v. *741Rockefeller, 336 F. Supp. 395, 398-400 (SD W. Va. 1972) (approving plan with 0.78% maximum deviation as justified by compactness provision in State Constitution); cf. Reynolds v. Sims, 377 U. S. 533, 579 (1964); Burns v. Richardson, 384 U. S. 73, 89, and n. 16 (1966). The State must, however, show with some specificity that a particular objective required the specific deviations in its plan, rather than simply relying on general assertions. The showing required to justify population deviations is flexible, depending on the size of the deviations, the importance of the State’s interests, the consistency with which the plan as a whole reflects those interests, and the availability of alternatives that might substantially vindicate those interests yet approximate population equality more closely. By necessity, whether deviations are justified requires case-by-case attention to these factors.
The possibility that a State could justify small variations in the census-based population of its congressional districts on the basis of some legitimate, consistently applied policy was recognized in Kirkpatrick itself. In that case, Missouri advanced the theory, echoed by Justice White in dissent, see post, at 771-772, that district-to-district differences in the number of eligible voters, or projected population shifts, justified the population deviations in that case. 394 U. S., at 534-535. We rejected its arguments not because those factors were impermissible considerations in the apportionment process, but rather because of the size of the resulting deviations and because Missouri “[a]t best. . . made haphazard adjustments to a scheme based on total population,” made “no attempt” to account for the same factors in all districts, and generally failed to document its findings thoroughly and apply them “throughout the State in a systematic, not an ad hoc, manner.” Id., at 535.11
*742The District Court properly found that appellants did not justify the population deviations in this case. At argument before the District Court and on appeal in this Court, appellants emphasized only one justification for the Feldman Plan’s population deviations — preserving the voting strength of racial minority groups.12 They submitted affidavits from *743Mayors Kenneth Gibson of Newark and Thomas Cooke of East Orange, discussing the importance of having a large majority of black voters in Newark’s Tenth District, App. 86-92, as well as an affidavit from S. Howard Woodson, Jr., a candidate for Mayor of Trenton, comparing the Feldman Plan’s treatment of black voters in the Trenton and Camden areas with that of the Reock Plan, id., at 93-96. See also id., at 82-83 (affidavit of A. Karcher). The District Court found, however:
“[Appellants] have not attempted to demonstrate, nor can they demonstrate, any causal relationship between the goal of preserving minority voting strength in the Tenth District and the population variances in the other districts. . . . We find that the goal of preserving minority voting strength in the Tenth District is not related in any way to the population deviations in the Fourth and Sixth Districts.” 535 F. Supp., at 982.
Under the Feldman Plan, the largest districts are the Fourth and Ninth Districts, and the smallest are the Third and Sixth. See supra, at 728. None of these districts borders on the Tenth, and only one — the Fourth — is even mentioned in appellants’ discussions of preserving minority voting strength. Nowhere do appellants suggest that the large population of the Fourth District was necessary to preserve minority voting strength; in fact, the deviation between the Fourth District and other districts has the effect of diluting the votes of all residents of that district, including members of racial minorities, as compared with other districts with fewer minority voters. The record is completely silent on the relationship between preserving minority voting *744strength and the small populations of the Third and Sixth Districts. Therefore, the District Court's findings easily pass the “clearly erroneous” test.
Y
The District Court properly applied the two-part test of Kirkpatrick v. Preisler to New Jersey’s 1982 apportionment of districts for the United States House of Representatives. It correctly held that the population deviations in the plan were not functionally equal as a matter of law, and it found that the plan was not a good-faith effort to achieve population equality using the best available census data. It also correctly rejected appellants’ attempt to justify the population deviations as not supported by the evidence. The judgment of the District Court, therefore, is
Affirmed.
[Map of New Jersey Congressional Districts follows this page.]
Three sets of census data are relevant to this case. In early 1981, the Bureau of the Census released preliminary figures showing that the total population of New Jersey was 7,364,158. In October 1981 it released corrected data, which increased the population of East Orange (and the State as a whole) by 665 people. Brief for Appellants 3, n. 1. All calculations in this opinion refer to the data available to the legislature — that is, the October 1981 figures. After the proceedings below had concluded, the Bureau of the Census made an additional correction in the population of East Orange, adding another 188 people, and bringing the total population of the State to 7,365,011. Ibid. Because this last correction was not available to the legislature at the time it enacted the plan at issue, we need not consider it.
In relevant part: “The House of Representatives shall be composed of Members chosen every second Year by the People of the several States ....
“Representatives . . . shall be apportioned among the several States which may be included within this Union, according to their respective Numbers . . . .”
There is some evidence in the record from which one could infer that this is precisely what happened in New Jersey. Alan Karcher, Speaker of the Assembly, testified that he had set one-percent maximum deviation as the upper limit for any plans to be considered seriously by the legislature, Record Doc. No. 41, pp. 56-58 (Karcher deposition), but there is no evi*732dence of any serious attempt to seek improvements below the one-percent level.
Such problems certainly apply to Justice White’s concededly arbitrary five-percent solution, see post, at 782, apparently selected solely to avoid the embarrassment of discarding the actual result in Kirkpatrick along with its reasoning. No de minimis line tied to actual population in any way mitigates differences identified post, at 771-772, between the number of adults or eligible, registered, or actual voters in any two districts. As discussed below, see infra, at 736-738, unless some systematic effort is made to correct the distortions inherent in census counts of total population, deviations from the norm of population equality are far more likely to exacerbate the differences between districts. If a State does attempt to use a measure other than total population or to “correct” the census figures, it may not do so in a haphazard, inconsistent, or conjectural manner. Kirkpatrick, 394 U. S., at 534-535; see infra, at 740-741.
Note that many of the problems that the New Jersey Legislature encountered in drawing districts with equal population stemmed from the decision, which appellees never challenged, not to divide any municipalities between two congressional districts. The entire State of New Jersey is divided into 567 municipalities, with populations ranging from 329,248 (Newark) to 9 (Tavistock Borough), See Brief for Appellants 36, n. 38. Preserving political subdivisions intact, however, while perfectly permissible as a secondary goal, is not a sufficient excuse for failing to achieve population equality without the specific showing described infra, at 740-741. See Kirkpatrick v. Preisler, supra, at 533-534; White v. Weiser, 412 U. S. 783, 791 (1973).
Justice White objects that “the rule of absolute equality is perfectly compatible with ‘gerrymandering’ of the worst sort,” Wells v. Rockefeller, 394 U. S. 542, 551 (1969) (Harlan, J., dissenting). Post, at 776. That may certainly be true to some extent: beyond requiring States to justify population deviations with explicit, precise reasons, which might be expected to have some inhibitory effect, Kirkpatrick does little to prevent what is known as gerrymandering. See generally Backstrom, Robins, & Eller, Issues in Gerrymandering: An Exploratory Measure of Partisan Gerrymandering Applied to Minnesota, 62 Minn. L. Rev. 1121, 1144-1159 (1978); cf. 394 U. S., at 534, n. 4. Kirkpatrick’s object, achieving population equality, is far less ambitious than what would be required to address gerrymandering on a constitutional level.
In any event, the additional claim that Kirkpatrick actually promotes gerrymandering (as opposed to merely failing to stop it) is completely empty. A federal principle of population equality does not prevent any State from taking steps to inhibit gerrymandering, so long as a good-faith effort is made to achieve population equality as well. See, e. g., Colo. Const. Art. V, § 47 (guidelines as to compactness, contiguity, boundaries of political subdivisions, and communities of interest); Mass. Const., Amended Art. CI, § 1 (boundaries); N. Y. Elec. Law § 4-100(2) (McKinney 1978) (compactness and boundaries).
Justice White further argues that the lack of a de minimis rule encourages litigation and intrusion by federal courts into state affairs. Post, at 777-778. It cannot be gainsaid that the de minimis rule he proposes would have made litigation in this case unattractive. But experience proves that cases in which a federal court is called upon to invalidate an existing apportionment, and sometimes to substitute a court-ordered plan in its stead, frequently arise not because a newly enacted apportionment plan fails to meet the test of Kirkpatrick, but because partisan politics frustrate the efforts of a state legislature to enact a new plan after a recent census has shown that the existing plan is grossly malapportioned. See, e. g., Carstens v. Lamm, 543 F. Supp. 68 (Colo. 1982); Shayer v. Kirkpatrick, *735541 F. Supp. 922 (WD Mo.), summarily aff’d, 456 U. S. 966 (1982); O’Sullivan v. Brier, 540 F. Supp. 1200 (Kan. 1982); Donnelly v. Meskill, 345 F. Supp. 962 (Conn. 1972); David v. Cahill, 342 F. Supp. 463 (NJ 1972); Skolnick v. State Electoral Board of Illinois, 336 F. Supp. 839 (ND Ill. 1971).
See generally J. Passel, J. Siegel, & J. Robinson, Coverage of the National Population in the 1980 Census, by Age, Sex, and Race: Preliminary Estimates by Demographic Analysis (Nov. 1981) (Record Doc. No. 31) (hereinafter Passel). Estimates for the national undercount in previous censuses range from 2.5% to 3.3%. See, e. g., Panel on Decennial Census Plans, Counting the People in 1980: An Appraisal of Census Plans 2 (Nat. Acad. Sciences 1978).
As an example, assume that in a hypothetical State with two congressional districts District A has a population of 502,500, and District B has a population of 497,500. The deviation between them is 5,000, or one percent of the mean. If the statewide undercount is also one percent, and it is distributed evenly between the two districts, District A will have a “real” population of 507,525, and District B will have a “real” population of 502,475. The deviation between them will remain one percent. Only if three-fourths of the uncounted people in the State live in District B will the two districts have equal populations. If three-fourths of the uncounted people happen to live in District A, the deviation between the two districts will increase to 1.98%.
For instance, it is accepted that the rate of undercount in the census for black population on a nationwide basis is significantly higher than the rate of undercount for white population. See generally Passel 9-20. Yet the census population of the districts in the Feldman Plan is unrelated to the percentage of blacks in each district. The Fourth District, for instance, is the largest district in terms of population, 0.268% above the mean; it has a 17.3% black population, App. 94. The First District is 14.6% black, id,., at 96, and it is almost exactly average in overall population. The undercount in any particular district cannot be predicted only from the percentage of blacks in the district, but to the extent that blacks are not counted, the undercount would be more severe in the Fourth District than in the relatively less populous First District.
According to the population figures used by Dr. Reock, the following adjustments to the Feldman Plan as enacted in Pub. L. 1982, ch. 1, would reduce its maximum population variance to 0.449%, somewhat lower than the version of the Reock Plan introduced in the legislature: To the Fifth District, add Oakland and Franklin Lakes (from the Eighth District), and Hillsdale, Woodcliff Lake, and Norwood (from the Ninth District). To the Sixth District, add North Brunswick (from the Seventh District). To the Seventh District, add Roosevelt (from the Fourth District), and South Plainfield and Helmett'a (from the Sixth District). To the Eighth District, add Montville and Boonton Town (from the Fifth District). To the Ninth District, add River Edge and Oradell (from the Fifth District).
Some of these changes are particularly obvious. Shifting the small town of Roosevelt from the Fourth to the Seventh District brings both appreciably closer to the mean, and the town is already nearly surrounded by the *740Seventh District. Similarly, River Edge, Oradell, Norwood, and Mont-ville are barely contiguous with their present districts and almost completely surrounded by the new districts suggested above. Further improvement could doubtless be accomplished with the aid of a computer and detailed census data. See also n. 5, supra.
We do not, of course, prejudge the validity of a plan incorporating these changes, nor do we indicate that a plan cannot represent a good-faith effort whenever a court can conceive of minor improvements. We point them out only to illustrate that further reductions could have been achieved within the basic framework of the Feldman Plan.
The very cases on which Kirkpatrick relied made clear that the principle of population equality did not entirely preclude small deviations caused by adherence to consistent state policies. See Swann v. Adams, 385 U. S. *742440, 444 (1967); Reynolds v. Sims, 377 U. S. 533, 579 (1964). District Courts applying the Kirkpatrick standard have consistently recognized that small deviations could be justified. See, e. g., Doulin v. White, 528 F. Supp. 1323, 1330 (ED Ark. 1982) (rejecting projected population shifts as justification for plan with 1.87% maximum deviation because largest district also had largest projected growth); West Virginia Civil Liberties Union v. Rockefeller, 336 F. Supp. 395, 398-400 (SD W. Va. 1972). Furthermore, courts using the Kirkpatrick standard to evaluate proposed remedies for unconstitutional apportionments have often, as in White v. Weiser, rejected the plan with the lowest population deviation in favor of plans with slightly higher deviations that reflected consistent state policies. See, e. g., David v. Cahill, 342 F. Supp. 463 (NJ 1972); Skolnick v. State Electoral Board of Illinois, 336 F. Supp., at 842-846. A number of District Courts applying the Kirkpatrick test to apportionments of state legislatures, before this Court disapproved the practice in Mahan v. Howell, 410 U. S. 315 (1973), also understood that justification of small deviations was a very real possibility. E. g., Kelly v. Bumpers, 340 F. Supp. 568, 571 (ED Ark. 1972), summarily aff’d, 413 U. S. 901 (1973); Ferrell v. Oklahoma ex rel. Hall, 339 F. Supp. 73, 84-85 (WD Okla.), summarily aff’d, 406 U. S. 939 (1972); Sewell v. St. Tammany Parish Police Jury, 338 F. Supp. 252, 255 (ED La. 1971). The court in Graves v. Barnes, 343 F. Supp. 704 (WD Tex. 1972)-later reversed by this Court for applying Kirkpatrick at all, White v. Regester, 412 U. S. 755 (1973)-characterized the inquiry required by Kirkpatrick as follows: “The critical issue remains the same: Has the State justified any and all variances, however small, on the basis of a consistent, rational State policy.” 343 F. Supp., at 713; see id., at 713-716.
At oral argument in this Court, appellants stated that the drafters of the Feldman Plan were concerned with a number of other objectives as well, namely “to preserve the cores of existing districts” and “to preserve municipal boundaries.” Tr. of Oral Arg. 4, 14. See also Answer and Counterclaim on Behalf of Alan J. Karcher ¶ 10 (Record Doc. No. 17). Similarly, Speaker Karcher’s affidavit suggests that the legislature was concerned that the Ninth District should lie entirely within Bergen County. App. 84. None of these justifications was presented to the District Court or this Court in any but the most general way, however, and *743the relevant question presented by appellants to this Court excludes them: “Whether the legislative policy of preserving minority voting strength justifies small deviations from census population equality in a congressional reapportionment plan.” Brief for Appellants i. Furthermore, several plans before the legislature with significantly lower population deviations kept municipalities intact and had an all-Bergen County Ninth District. See App. 66-74.