This is the first of four consolidated cases we decide today.1 In all of them, black voters challenge municipal election schemes that provide for the at-large election of certain city officials. The gravamen of their claims is that the black vote in each of the municipalities is, submerged in an unnecessarily large, city-wide electorate and ■consequently that they are unconstitutionally deprived of their right to effective political participation in each of these cities.
Black residents of Fairfield, an industrial suburb of Birmingham, Alabama, brought this action to strike down their city’s municipal election system, which provides for the at-large selection of a city council president and city councilmen.2 These plaintiffs (appellants here) claim that Fairfield’s at-large system, as applied, acts to dilute their voting power in violation of the fourteenth and fifteenth amendments to the Constitution.3
A council consisting of twelve aldermen and a president governs the City of Fair-field. State law allows cities the size of Fairfield, which had a population of 14,369 in 1970 (forty-eight percent of which was black), to divide themselves into wards for the purpose of city government.4 Cities *214may choose the number of wards and thereby determine whether the aldermen (who must reside in their respective wards) are elected at-large or separately from their wards. Fairfield sectioned itself into six wards and was thus required to elect at-large two aldermen from each ward.5
Prior to 1968, no black had been elected to the city council, but in that year six of the seven black candidates succeeded. In 1972, none of the eight black candidates were elected to the council. According to the district court, these disparate election results can be attributed to racially polarized voting by an electorate in close and changing racial balance.6
The complaint in this action was filed on May 30, 1973, alleging that “such absolute control of the city government by one race” in an at-large setting worked an unconstitutional dilution of black votes. The case was tried on February 20, 1975, and, after the consideration of voluminous evidence, the district court ruled in favor of the plaintiffs, dictated into the record its findings of fact and conclusions of law, and ordered the parties to file reapportionment plans by May 1, 1975. The parties submitted plans and a hearing was held to consider them. The district court entered its final judgment on June 6, 1975, ordering the city divided into eight single-member council districts but allowing the at-large election of a city council president.7 The judgment was appealed, and on June 8, 1976, a panel of this court vacated and remanded it, Nevett v. Sides, 533 F.2d 1361 (5th Cir. 1976), for failing to apply properly the voting dilution standards set forth in Zimmer v. McKeithen, 485 F.2d 1297 (5th Cir. 1973) (en banc), aff’d sub nom. East Carroll Parish School Board v. Marshall, 424 U.S. 636, 96 5. Ct. 1083, 47 L.Ed.2d 296 (1976),8 where we enunciated a set of factors that when established in the aggregate, are probative of unconstitutional dilution.
The district court’s error was that having found “the various standards and indicia prescribed by the appellate court [not] helpful one way or the other,” it nevertheless held that the plan unintentionally “does act to inhibit and has inhibited voting strength” and that “in practice it has worked that way.” We held this finding insufficient to support a conclusion of unconstitutional dilution. A finding of dilution, we noted,
must be based on the criteria that the Zimmer and Wallace [v. House, 515 F.2d 619 (5th Cir. 1975), vacated and remanded on other grounds, 425 U.S. 947, 96 S.Ct. 1721, 48 L.Ed.2d 191 (1976)] courts distilled from White v. Regester, 412 U.S. 755, 765-767, 93 S.Ct. 2332, 2339-2340, 37 L.Ed.2d 314, 324-325 (1973) and in accordance with all later cases. Unless those criteria in the aggregate point to dilution, i. e., if the criteria ‘don’t really *215help’, then plaintiffs have not met their burden, and their cause must fail.
Nevett v. Sides, 533 F.2d at 1365.
On remand, the district court carefully reexamined its findings of fact (no additional evidence was taken by the court) and considered the Zimmer criteria with specificity.9 The court ultimately concluded that those findings did not demonstrate an unconstitutional dilution of the black vote in Fairfield. Judgment was entered for the defendants on June 11, 1976, and the plaintiffs took this appeal.
In this appeal, the parties present the following issues for our determination: (1) whether a finding of intentional discrimination is required in a voting dilution case brought by a racial group, (2) whether the district court’s findings of fact under the Zimmer criteria are reversible, and (3) whether the district court as a matter of law correctly interpreted Zimmer and subsequent relevant precedents. Since these issues are complex and significant, we think it appropriate to outline briefly how our analysis will proceed.
In Part I we discuss the nature of voting dilution cases and the legal principles governing their determination. This discussion provides the necessary background for Part II, where we examine the first issue raised here, whether intentional discrimination need be shown to make out a case alleging dilution of the voting power of a cognizable racial element. We hpldylhat a showing of intent is necessary to establish such a case.
Our holding is based on consideration of both the fourteenth and fifteenth amendments. We determine that the recent Supreme Court decision in Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976), requires a showing of intentional discrimination in racially based voting dilution claims founded on the fourteenth amendment. We conclude also that the case law requires the same showing in fifteenth amendment dilution claims. Moreover, we demonstrate that the dilution cases of this circuit are consistent with our holding in this case. In particular, we read Zimmer as impliedly recognizing the essentiality of intent in dilution cases by establishing certain categories of circumstantial evidence of intentional discrimination.
Having set out the relevant legal principles, the focus of our discussion shifts in Part III to the specifics of this case. There we address and dismiss appellants’ contention that the district court’s factual determinations are clearly erroneous. Finally, in Part IV we reject appellants’ argument that the court below misinterpreted the dilution precedents of this circuit. Consequently, we affirm the judgment of the district court.
I. Voting Dilution
In describing voting dilution claims, it is imperative at the outset to distinguish the typical reapportionment case, which presents the traditional “one person, one vote” inquiry. See Reynolds v. Sims, 377 U.S. 533, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964). In such a case, there are a number of coordinate districts (e. g., state legislative districts), and voters in larger districts allege that their votes are devalued in comparison to those of voters in smaller ones. The issue in a typical reapportionment case, therefore, is whether population deviations from the average district are impermissibly large. See, e. g., White v. Regester, 412 U.S. 755, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973); Gaffney v. Cummings, 412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973); Mahan v. Howell, 410 U.S. 315, 93 S.Ct. 979, 35 L.Ed.2d 320 (1973). The comparison is one based purely on population figures; no showing of discrimination along racial, ethnic, or political lines need be shown.
A case alleging violation of the one person, one vote standard, based solely on a mathematical analysis, may properly be called a “quantitative” reapportionment case. That an apportionment scheme satisfies the quantitative standard does not, however, insure equality in all the aspects of political representation. The hetero*216geneity of our society manifests itself in an unequal distribution of interest groups; racial and ethnic groups tend to be compartmentalized. Thus, even a districting plan drawn without regard to the distribution of such groups may distort their relative voting strengths. And, of course, these underlying patterns present the opportunity for subtle discrimination by the manipulation of district lines. Such discrimination can occur even if perfect population equality exists. Cases alleging a distortion of group voting power of this type have been termed “qualitative” reapportionment cases because they focus “not on population-based apportionment but on the quality of representation.” Whitcomb v. Chavis, 403 U.S. 124, 142, 91 S.Ct. 1858, 1868, 29 L.Ed.2d 363 (1971).
A familiar type of qualitative reapportionment case is one alleging gerrymander, the drawing of district lines to fence out, e. g., Gomillion v. Lightfoot, 364 U.S. 339, 81 S.Ct. 125, 5 L.Ed.2d 110 (1960), or slice up a compact interest group, e. g., Kirksey v. Board of Supervisors, 554 F.2d 139 (5th Cir.) (en banc), cert. denied,- U.S. -, 98 S.Ct. 512, 54 L.Ed.2d 454 (1977). Another, similar variety of qualitative reapportionment case is the dilution case, such as the one presented here. An at-large scheme operating to dilute the voting efficacy of an interest group does so by exploiting the tendency of large districts to diminish what would be the natural effect of residency patterns if legitimate single-member districts were employed instead. If the single-member districts are small enough, a compact interest group will constitute a majority in some districts and will thus have the capacity to elect candidates sympathetic to its needs. The large districts characteristic of at-large plans tend to submerge compact groups in constituencies whose predominant segments may be unsympathetic to the group and its needs.
The Constitution, however, does not demand that each cognizable element of a constituency elect representatives in proportion to its voting strength. White v. Regester; Whitcomb v. Chavis; Kirksey v. Board of Supervisors; Zimmer v. McKeithen. Even consistent defeat of a group’s candidates, standing alone, does not cross constitutional bounds. Whitcomb v. Chavis, 403 U.S. at 152-53, 91 S.Ct. 1858.
The issue in dilution cases, therefore, is not whether a given group elects a minimum number of candidates, and the standards are not different when, as here, the interest binding the group is one of race. “[I]t is not enough that the racial group allegedly discriminated against has not had legislative seats in proportion to its voting potential.” White v. Regester, 412 U.S. at 765-66, 93 S.Ct. at 2339. Rather, in the absence of evidence that the at-large provisions themselves were “conceived or operated as purposeful devices to further racial . discrimination,” Whitcomb v. Chavis, 403 U.S. at 149, 91 S.Ct. at 1872, the inquiry becomes one of determining whether the influence of a given racial group has been distorted because its members have been denied equal access to political processes such as party nominating procedures, registration, and, of course, voting. See id. at 149-50, 91 S.Ct. 1858. As explained in White v. Regester, the only Supreme Court case to date that has struck down an at-large scheme under a dilution rationale,
[t]he plaintiffs’ burden is to produce evidence to support findings that the political processes leading to nomination and election were not equally open to participation by-the group in question — that its members had less opportunity than did other residents in the district to participate in the political processes and to elect legislators of their choice.
White v. Regester, 412 U.S. at 766, 93 S.Ct. at 2339, (citing Whitcomb v. Chavis, 403 U.S. at 149-50, 91 S.Ct. 1858).
In Zimmer v. McKeithen this circuit explicated the tests established in Chavis and Regester by enumerating certain factors the district courts should consider to determine whether a dilution case has been made out. These criteria were designed to guide the district court in the reception of evidence by establishing certain inquiries sub*217sidiary to the ultimate issue of dilution. The district court is to make a particularized determination under each criterion and then weigh its findings to ascertain whether “in the aggregate” they point to dilution. Hendrix v. Joseph, 559 F.2d 1265 (5th Cir. 1977); David v. Garrison, 553 F.2d 923, 929 (5th Cir. 1977); Nevett v. Sides, 533 F.2d 1361, 1365 (5th Cir. 1976); Zimmer, 485 F.2d at 1305.
The court in Zimmer established two categories, one containing criteria going primarily to the issue of denial of access or dilution, the other containing inquiries as to the existence of certain structural voting devices that may enhance the underlying dilution. The “primary” factors include: the group’s accessibility to political processes (such as the slating of candidates), the responsiveness of representatives to the “particularized interests” of the group, the weight of the state policy behind at-large districting, and the effect of past discrimination upon the group’s participation in the election system. 485 F.2d at 1305. The “enhancing” factors include: the size of the district; the portion of the vote necessary for election (majority or plurality); where the positions are not contested for individually, the number of candidates for which an elector must vote10; and whether candidates must reside in subdistricts. Id.
The following discussion demonstrates that a finding of racially discriminatory dilution under the Zimmer criteria raises an inference of intent and, therefore, that a finding under the criteria satisfies the intent requirement of Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976). Before this discourse is set out, we will examine the relevance of Davis to the voting dilution principle.
II. The Intent Requirement in Voting Dilution Gases
In this part we explain and justify our holding that to succeed in a dilution case such as the one before us, a plaintiff must show the at-large plan to be racially motivated. We begin with a discussion of the applicability of the intent principle to fourteenth amendment dilution claims. Next, the applicability of the principle to fifteenth amendment claims is discussed. Finally, we harmonize our holding with the case law of this circuit by demonstrating that Zimmer and its progeny establish sufficient conditions .for a finding of intentional discrimination.
A. Intent in Fourteenth Amendment Dilution Claims
We start with a reiteration of the principle expounded by the Supreme Court in Davis. Where official action is racially neutral on its face, courts must adhere “to the basic equal protection principle that the invidious quality of a law claimed to be racially discriminatory must ultimately be traced to a racially discriminatory purpose.” 426 U.S. at 240, 96 S.Ct. at 2048; accord, United States v. Texas Education Agency, 564 F.2d 162, 165-66 (5th Cir. 1977). The Court restated this teaching in Village of *218Arlington Heights v. Metropolitan Housing Development Corp., 429 U.S. 252, 265, 97 S.Ct. 555, 563, 50 L.Ed.2d 450 (1977): “Proof of racially discriminatory intent or purpose is required to show a violation of the Equal Protection Clause.” The language of Davis and Arlington Heights appears to establish intent as a prerequisite of universal applicability to fourteenth amendment claims of racial discrimination.11 For appellants to succeed in their assertion that racially discriminatory intent need not be shown in dilution cases, we must find such cases exempt from the general principle enunciated in Davis and Arlington Heights. We do not so find.
It is readily apparent that voting dilution cases are quite typical of traditional fourteenth amendment cases. Here the appellants challenge legislation establishing at-large districting, a practice racially neutral on its face, as discriminatory in its effect: blacks do not elect their proportionate share of the city council. In Davis, the plaintiffs attacked a written personnel test, itself devoid of racial overtones, that had the effect of failing four times as many blacks as whites. And in Arlington Heights, blacks challenged a zoning ordinance prohibiting multi-family development, again a neutral provision, that resulted in the virtual exclusion of racial minority groups. The plaintiffs failed in both of these latter cases because they had not shown the official action to be racially motivated. Simply put, “[p]roof of a racially discriminatory intent or purpose is required to show a violation of the Equal Protection Clause.”
The language of the Court in Davis and Arlington Heights is unambiguous and admits of no exception. Analytically, nothing about at-large districting legislation suggests that it should be treated differently from any other manifestation of official action that may impact groups of people differentially. This observation is substantiated by the reliance of the Court in Davis and Arlington Heights upon Wright v. Rockefeller, 376 U.S. 52, 84 S.Ct. 603, 11 L.Ed.2d 512 (1964), a case that entertained an allegation that New York’s congressional apportionment plan was a racial gerrymander.
In Davis and Arlington Heights, the Court buttressed its holdings by referring to Wright and other fourteenth amendment cases that held intentional discrimination necessary. The Davis opinion contains the following discussion:
The rule is the same in other contexts. Wright v. Rockefeller, 376 U.S. 52, 84 S.Ct. 603, 11 L.Ed.2d 512 (1964), upheld a New York congressional apportionment statute against claims that district lines had been racially gerrymandered. The challenged districts were made up predominantly of whites or of minority races, and their boundaries were irregularly drawn. The challengers did not prevail because they failed to prove that the New York legislature ‘was either motivated by racial considerations or in fact drew the districts on racial lines’; the plaintiffs had not shown that the statute ‘was the product of a state contrivance to segregate on the basis of race or place of origin.’ 376 U.S. at 56, 58, 84 S.Ct. at 605, 11 L.Ed.2d, at 515. The dissenters were in agreement that the issue was whether the ‘boundaries . . . were purposefully drawn on racial lines.’ 376 U.S. at 67, 84 S.Ct. at 611, 11 L.Ed.2d at 522.
426 U.S. at 240, 96 S.Ct. at 2047; accord, Arlington Heights, 429 U.S. at 265, 97 S.Ct. 555.
This very recent reaffirmation of the holding in Wright leaves no doubt that a showing of intent is a necessary element in a case alleging a racial gerrymander.12 We see no distinction that would *219call for different constitutional requisites in a racial gerrymander case than in a voting dilution case such as this. The right allegedly infringed is the same in both contexts: the right to effective participation in the electoral process. An unconstitutional gerrymander violates this right by compartmentalizing or fencing out a group, e. g., Gomillion v. Lightfoot, 364 U.S. 339, 81 S.Ct.. 125, 5 L.Ed.2d 110 (1960), or by slicing up a compact minority, e. g., Kirksey v. Board of Supervisors, 554 F.2d 139 (5th Cir.) (en bane), cert. denied, - U.S. -, 98 S.Ct. 512, 54 L.Ed.2d 454 (1977); Robinson v. Commissioners Court, 505 F.2d 674 (5th Cir. 1974). An invidious at-large scheme merely achieves the same end, denial of effective participation, by submerging an interest group in a constituency large enough and polarized enough to place that group in the minority consistently.
That the constitutional tests should be the same whether the right to an equally effective vote is denied by drawing district lines or erasing them is illustrated in a number of our cases. We have repeatedly held the Zimmer criteria relevant to gerrymander as well as dilution cases. In Robinson v. Commissioners Court, 505 F.2d 674 (5th Cir. 1974), a case finding a racially motivated gerrymander that fragmented “what could otherwise be a cohesive voting community,” id. at 679, we stated:
The standards for decision in dilution cases are developed primarily in cases dealing with [at-large] districting [citing, inter alia, White v. Regester, Whitcomb v. Chavis, and Zimmer v. McKeithen]. But “we have no hesitation in applying [those tests to] measure . . the constitutionality of reapportionment plans involving only single-member districts. In each instance, we are required to determine the same question, whether or not there has been an unconstitutional manipulation of electoral district boundaries so as to minimize or dilute the voting strength of a minority class or interest.”
Id. at 678 (quoting Howard v. Adams County Board of Supervisors, 453 F.2d 455, 458 n. 2 (5th Cir.), cert. denied, 407 U.S. 925, 92 S.Ct. 2461, 32 L.Ed.2d 812 (1972)) (emphasis added); accord, Kirksey v. Board of Supervisors, 554 F.2d at 143. Since we find no constitutionally significant distinction between this case and a gerrymander case like Wright v. Rockefeller, a decision expressly reaffirmed by the Supreme Court in Davis and Arlington Heights, we hold that a showing of racially motivated discrimination is a necessary element in an equal protection voting dilution claim such as the one presented in this case.13
*220B. Intent in Fifteenth Amendment Dilution Claims
The appellants allege that Fair-field’s at-large plan is violative of the fifteenth amendment as well as the fourteenth. Thus, we must determine whether illicit motivation is a prerequisite to a successful claim under the fifteenth amendment. We hold that it is.
The fifteenth amendment is a specific prohibition against state or federal action that denies or abridges “[t]he right of citizens of the United States to vote . on account of race, color, or previous condition of servitude.” U.S.Const. amend. XV, § 1. Historically, this amendment was the vehicle of first resort for blacks alleging impairment of their franchise.14 It protects the rights of blacks to participate at all levels of the political process and interdicts all methods demonstrably contrived to diminish this participation.15 As the Supreme Court stated in the case of Lane v. Wilson, 307 U.S. 268, 275, 59 S.Ct. 872, 876, 83 L.Ed. 1281 (1939):
The [Fifteenth] Amendment nullifies sophisticated as well as simple-minded modes of discrimination. It hits onerous procedural requirements which effectively handicap exercise of the franchise by the colored race although the abstract right to vote may remain unrestricted as to race.
Broad though the reach of the amendment may be, it has been invoked successfully only in cases founded on acts of intentional racial discrimination. The necessary motivation was painfully apparent in the early cases striking down the exclusion of blacks from party primaries, e. g., Terry v. Adams, 345 U.S. 461, 463-65, 73 S.Ct. 809, 97 L.Ed. 1152 (1953); the grandfather clause, Guinn v. United States, 238 U.S. 347, 364-66, 35 S.Ct. 926, 59 L.Ed. 1340 (1915); and the invidious administration of literacy tests, e. g., Louisiana v. United States, 380 U.S. 145, 151-53, 85 S.Ct. 817, 13 L.Ed.2d 709 (1965). Moreover, and of particular relevance to the inquiry before us, racially *221discriminatory motivations were unmistakably present in Gomillion, where the Court remarked that if the plaintiffs could prove their allegations,
the conclusion would be irresistable, tantamount for all practical purposes to a mathematical demonstration, that the legislation is solely concerned with segregating white and colored voters by fencing Negro citizens out of town so as to deprive them of their pre-existing municipal vote.
364 U.S. at 341, 81 S.Ct. at 127. These cases illustrate what is apparent on the face of the amendment: a showing of racially motivated official action that infringes the right to vote is sufficient to state a cause of action.
Our holding is the converse of this proposition. A showing of improper motivation or purpose is necessary to establish a valid cause of action under the fifteenth amendment. Our conclusion is compelled by Wright, the Supreme Court decision we have held controlling on the issue of intent in the fourteenth amendment claims in this case. Wright was brought under the fifteenth amendment as well. 376 U.S. at 56, 84 S.Ct. 603. That the Court held a showing of intentional discrimination was essential to a valid claim in that case implies as a matter of logic that such a demonstration is necessary under both fourteenth and fifteenth amendments.
Cases in this circuit exemplify the teaching of Wright. In Bradas v. Rapides Parish Police Jury, 508 F.2d 1109 (5th Cir. 1975), we vacated and remanded a judgment finding an at-large plan violative of the fifteenth amendment. Writing for the court, Judge Simpson stated:
it does not suffice to show that the use of [at-large] districts has diminished to some extent the proportion of blacks in the voting unit unless some evidence also demonstrates that such [at-large] districts were “conceived or operated as purposeful devices to further racial or economic discrimination.”
Id. at 1113 (quoting Whitcomb v. Chavis, 403 U.S. at 149, 91 S.Ct. 1858); see Paige v. Gray, 538 F.2d 1108 (5th Cir. 1976).
We have held that the appellants cannot succeed on either their fourteenth or fifteenth amendment claims unless they establish that Fairfield’s at-large method of electing its city council exists because of invidious racial motivations. In the following section we demonstrate that the controlling dilution precedents of this circuit are consistent with this holding.
C. Fifth Circuit Dilution Precedents
The Alabama statute enabling Fairfield to establish its at-large electoral scheme was enacted in 1909. In 1901, however, Alabama had adopted a constitution which had effectively disenfranchised blacks. The appellees contend, therefore, that the 1909 statute could not have been adopted with a racial animus because no blacks who could have been discriminated against could vote. See McGill v. Gadsden County Commission, 535 F.2d 277, 279-80 (5th Cir. 1976); Taylor v. McKeithen, 499 F.2d 893 (5th Cir. 1974). Although we accept the district court’s finding that the 1909 plan was adopted without discriminatory intent, cases of this circuit emphasize that the search for improper motivation does not end at the enacting stage. Thomasville Branch of the NAACP v. Thomas County, 571 F.2d 257 (5th Cir. 1978). A plan, racially neutral at its adoption, may further preexisting intentional discrimination, e. g., Kirksey, or it may be maintained for invidious purposes, e. g., Bolden v. City of Mobile, 571 F.2d 238 (5th Cir. 1978).
Whether invidious discrimination motivates the adoption or maintenance of a districting scheme or whether the plan furthers preexisting purposeful discrimination, the intent requirement may be satisfied by direct or circumstantial evidence. Where direct evidence of discriminatory motive is proffered, a case is easily made, see, e. g., Terry v. Adams, 345 U.S. 461, 73 S.Ct. 809, 97 L.Ed. 1152 (1953), as it is where the circumstantial evidence of racially discriminatory motivation is so strikingly obvious that no alternative explanation is plausible, e. g., Gomillion; Yick Wo v. Hopkins, 118 *222U.S. 356, 6 S.Ct. 1064, 30 L.Ed. 220 (1886). “But such cases are rare. Absent a pattern as stark as that in Gomillion or Yick Wo, impact alone is not determinative, and the Court must look to other evidence.” Arlington Heights, 429 U.S. at 266, 97 S.Ct. at 564 (footnotes omitted). An examination of the Zimmer factors shows that they constitute “other evidence” that a court must consider in determining whether the districting scheme exists because of invidious racial considerations.
The Zimmer criteria go to the issue of intentional discrimination, first of all, because they would be irrelevant if motivation were not an issue. If, as the appellants suggest, it is sufficient that “the combination of a legal system (at-large election) with the minority status of blacks and a societal system (racially polarized voting) has the effect of diluting black voting strength” then of what relevance is the accessibility of political processes to blacks, the responsiveness of the city council to the needs of blacks, the weight of the state policy behind the at-large plan, or the existence of past discrimination in the electoral process? Moreover, the Supreme Court has squarely rejected the contention that at-large elections are unconstitutional merely because fewer minority candidates are elected, due to polarized voting, than would correspond to the minority’s portion of the district population. Whitcomb v. Chavis, 403 U.S. 124, 91 S.Ct. 1858, 29 L.Ed.2d 363 (1971). It is clear, therefore, that mere disproportionate effects are not enough to invalidate an at-large plan and'hence that the Zimmer criteria purport to establish something more.
Perhaps the most useful approach to analyzing the Zimmer criteria as they relate to the existence of intentional discrimination is to assume that an at-large scheme is being used as a vehicle for achieving the constitutionally prohibited end. The objective of such a scheme would be to prevent a group from effectively participating in elections so that the governing body need not respond to the group’s needs. This objective would be achieved by insuring that a cohesive group remains a minority in the voting population, thus preventing that group from electing minority representatives or from holding nonminority representatives accountable.
Circumstantial evidence that the plan was enacted with discriminatory intent may exist in the form of starkly differential racial impact; the historical background of the plan, “particularly if it reveals a series of official actions taken for invidious purposes”; or the “specific sequence of events leading up to the challenged decision.” Arlington Heights, 429 U.S. at 267, 97 S.Ct. at 564; see Smith v. Paris, 257 F.Supp. 901 (M.D.Ala.1966), aff’d per curiam, 386 F.2d 979 (5th Cir. 1967); Sims v. Baggett, 247 F.Supp. 96 (M.D.Ala.1965). Such was the approach of the inquiries in Davis and Arlington Heights, cases we noted recently in Kirksey v. Board of Supervisors to be “of particular significance ... if the only issue were whether the racially neutral plan created such exclusion [from the electoral process].” 554 F.2d at 147 (emphasis in original). But, as we held in Kirksey, the inquiry does not stop at the enacting stage.
Where evidence of discriminatory intent is lacking in the enacting processes, the Zimmer criteria become acutely relevant. They may demonstrate, as in Kirksey, that the neutral plan is an “instrumentality for carrying forward patterns of purposeful and intentional discrimination.” 554 F.2d at 147. In Kirksey, the plan was recently formulated, and it perpetuated past intentional discrimination. A remotely enacted plan, such as the 1909 plan in this case, that was adopted without racial motivations may become a vehicle for the exclusion of meaningful minority input because intervening circumstances cause the plan to work that way. When the more blatant obstacles to black access are struck down, such an at-large plan may operate to devalue black participation so as to allow representatives to ignore black needs. Where the plan is maintained with the purpose of excluding minority input, the necessary intent is established, and the plan is unconstitutional. We so hold today in Bolden v. City of Mobile.
*223Whether the plan is recent or remote, the Zimmer criteria provide a factual basis from which the necessary intent may be inferred. Consider a plan neutral in its enactment that is used as a vehicle for intentionally ignoring black interests. The existence of such discrimination presupposes racially polarized voting in the electorate.16 Polarized or bloc voting, although in itself constitutionally unobjectionable17, allows representatives to ignore minority interests without fear of reprisal at the polls. When bloc voting has been demonstrated,18 a showing under Zimmer that the governing body is unresponsive to minority needs is strongly corroborative of an intentional exploitation of the electorate’s bias. The likelihood of intentional exploitation is “enhanced” by the existence of systemic devices such as a majority vote requirement, an anti-single shot provision, and the lack of a requirement that representatives reside in subdistricts. Zimmer, 485 F.2d at 1305. As the Supreme Court observed, “[tjhese characteristics of [an] electoral system, neither in themselves improper nor invidious, [enhance] the opportunity for racial discrimination . . . .” White v. Regester, 412 U.S. at 766, 93 S.Ct. at 2340.
The establishment under Zimmer that blacks have been denied access to slating, registration, or other aspects of political participation may indicate that if white representatives have not properly entertained black interests, it is because blacks cannot achieve the input to which they are entitled.. See Wallace v. House, 515 F.2d 619, 622-23 (5th Cir. 1975), vacated and remanded on other grounds, 425 U.S. 947, 96 S.Ct. 1721, 48 L.Ed.2d 191 (1976). Under the proper circumstances, such a showing would satisfy the intent requirement.19
*224A tenuous state policy in favor of at-large districting may constitute evidence that other, improper motivations lay behind the enactment or maintenance of the plan. The absence of a significant and legitimate state policy behind districting provisions has been an important factor in several cases finding intentional discrimination. In Gomillion, the defendant city officials had “never suggested, either in their brief or in oral argument, any countervailing municipal function which [the districting act] is designed to serve.” 364 U.S. at 342, 81 S.Ct. at 127. And in Guinn v. United States, 238 U.S. 347, 35 S.Ct. 926, 59 L.Ed. 1340 (1915), which struck down Oklahoma’s grandfather clause, the Court stated: “we are unable to discover how, unless the prohibitions of the 15th Amendment were considered, the slightest reason was afforded for basing the classification upon a period of time prior to the 15th Amendment.” Id. at 366, 35 S.Ct. at 931. Although state statutes generally need satisfy only minimum rationality requirements, see, e. g., Hennessey v. National Collegiate Athletic Association, 564 F.2d 1136, 1144 (5th Cir. 1977), the weight of the state policy behind the districting plan is an evidentiary consideration that must be considered along with all other relevant evidence to determine whether the plan is improperly motivated.20
That the finder of fact determines the plaintiff has prevailed under one or even several of the Zimmer criteria may not establish the existence of intentional discrimination. See, e. g., McGill v. Gadsden County Commission, 535 F.2d 277 (5th Cir. 1976). The evidence under the other criteria may weigh so heavily in favor of the defendant that the evidence as a whole will not bear an inference of invidious discrimination. Of course, the plaintiff need not prevail under all of the criteria, Zimmer, 485 F.2d at 1305, nor is he limited to them.21 The task before the fact finder is to determine, under all the relevant facts, in whose favor the “aggregate” of the evidence preponderates.22 This determination is peculiarly dependent upon the facts of each case. It comprehends “a blend of history and an intensely local appraisal of the design and impact of the [at-large] district in the light of past and present reality, political and otherwise.” White v. Regester, 412 U.S. at 769-70, 93 S.Ct. at 2341. It is the obligation, therefore, of the finder of fact carefully to examine and weigh the competing factors to determine whether the coincidence of those probative of intentional discrimination is sufficient. “Determining whether invidious discriminatory purpose was a motivating factor demands a sensitive inquiry into such circumstantial and direct evidence of intent as may be availa*225ble.” Arlington Heights, 429 U.S. at 266, 97 S.Ct. at 564.
We take this opportunity to address language in several opinions of this circuit that has caused some apparent confusion in this changing and complex area of the law. It appears that a number of our cases have espoused alternative approaches available to plaintiffs in dilution cases. The earliest case setting forth these alternatives is Howard v. Board of Supervisors, 453 F.2d 455 (5th Cir.), cert. denied, 407 U.S. 925, 92 S.Ct. 2461, 32 L.Ed.2d 812 (1972).
As we view the constitutional requirements in this area, to establish the existence of a constitutionally impermissible redistricting plan, in the absence of malapportionment, plaintiffs must maintain the burden of proving (1) a racially motivated gerrymander, or a plan drawn along racial lines, Wright v. Rockefeller, 1964, 376 U.S. 52, 84 S.Ct. 603, 11 L.Ed.2d 512; Gomillion v. Lightfoot, 1960, 364 U.S. 339, 81 S.Ct. 125, 5 L.Ed.2d 110; Sims v. Baggett, M.D.Ala.1965, 247 F.Supp. 96, or (2) that . designedly or otherwise, a[n] . . .apportionment scheme, under the circumstances of a particular case, would operate to minimize or cancel out the .voting strength of racial or political elements of the voting population.” Burns v. Richardson, 1966, 384 U.S. 73, 88, 86 S.Ct. 1286, 1294, 16 L.Ed.2d 376. See Whit-comb v. Chavis, 1971, 403 U.S. 124, 143-144, 149, 91 S.Ct. 1858, 29 L.Ed.2d 363.
Id. at 457-58 (emphasis in original) (footnote omitted). Subsequent decisions have reiterated these standards. Panior v. Iberville Parish School Board, 536 F.2d 101, 104-05 (5th Cir. 1976); Ferguson v. Winn Parish Police Jury, 528 F.2d 592, 596-97 (5th Cir. 1976); Wallace v. House, 515 F.2d 619, 622-23 (5th Cir. 1975), vacated and remanded on other grounds, 425 U.S. 947, 96 S.Ct. 1721, 48 L.Ed.2d 191 (1976); Bradas v. Rapides Parish Police Jury, 50.8 F.2d 1109, 1113 (5th Cir. 1975); Robinson v. Commissioners Court, 505 F.2d 674, 678 n. 3 (5th Cir. 1974); Moore v. Leflore County Board of Election Commissioners, 502 F.2d 621, 623-24 (5th Cir. 1974); Zimmer, 485 F.2d at 1304.
The first approach open to plaintiffs is one we have already discussed. Blacks challenging a districting system may succeed under a Gomillion-type rationale by establishing that the plan was enacted with discriminatory purpose. The second avenue, however, seems to allow plaintiffs to succeed under a dilution rationale without establishing intentional discrimination. To the extent that these cases suggest that intent is not required, they cannot be reconciled with the intervening Supreme Court decisions in Davis and Arlington Heights.
In each of these Fifth Circuit cases, however, such language was not operative. In Robinson v. Commissioners Court, the plan was struck down under the first alternative: intentional discrimination was found. “The district court determined .- that the County Commissioners' apportionment was designed precisely to dilute the black vote and ... we find no reason on this record to reject that conclusion as clearly erroneous.” 505 F.2d at 679 (emphasis added). Those cases finding dilution under the second alternative did so on the basis of Zimmer. Wallace v. House, 515 F.2d at 623-24; Moore v. Leflore County Board of Election Commissioners, 502 F.2d at 624-25; cf. Ferguson v. Winn Parish Police Jury, 528 F.2d at 598-99. We hold today that a finding of dilution under Zimmer raises an inference of intentional discrimination, and, therefore, the essential element of intent was present in each of these cases. Finally, cases finding no dilution, like Howard v. Board of Supervisors, Panoir v. Iberville Parish School Board, and Bradas v. Rapides Parish Police Jury, cannot establish the proposition that intent is unnecessary to make out a dilution case.
Having determined that plaintiffs must make a showing of intentional discrimination to prevail in a dilution case, and having set forth the means of establishing the requisite showing, we now turn to the specifics of this case to measure it against the standards we have enunciated.
III. The District Court’s Findings of Fact
We now address the second issue raised on appeal: whether the district *226court’s findings of fact with respect to the Zimmer criteria are erroneous. We must preface our inquiry with the principle that the district court’s determinations under the Zimmer criteria will stand, if supported by sufficient evidence, unless clearly erroneous. Fed.R.Civ.P. 52(a); Hendrix v. Joseph, 559 F.2d 1265, 1268 (5th Cir. 1977); Gilbert v. Sterrett, 509 F.2d 1389, 1393 (5th Cir. 1975); see McGill v. Gadsen County Commission, 535 F.2d 277, 280 (5th Cir. 1976). Additionally, the panel hearing this case on the first appeal had occasion to examine the district court’s findings of fact, which have not been augmented by any new evidence on remand, and it determined that “[n]one of the findings of fact, considered separately from the intermingled conclusions of law, can be set aside as clearly erroneous.” 533 F.2d at 1364. We accept this court’s prior appraisal as law of the case with respect to the factual matters determined by the district court in its original, February 20, 1975, opinion. See Carpa, Inc. v. Ward Foods, Inc., 567 F.2d 1316, 1319-1321 (5th Cir. 1978); Lincoln National Life Insurance Co. v. Roosth, 306 F.2d 110 (5th Cir. 1962), cert. denied, 372 U.S. 912, 83 S.Ct. 726, 9 L.Ed.2d 720 (1963).
The only question remaining, then, is whether the latest, June 11, 1976, findings of the district court are consistent with its prior finding^. We proceed by examining the district court’s determinations under each of the Zimmer criteria that appellants’ challenge on this appeal. First, however, we think it profitable to take this opportunity briefly to discuss what Zimmer requires of a trial court in a dilution case.
The ultimate issue in a case alleging unconstitutional dilution of the votes of a racial group is whether the districting plan under attack exists because it was intended to diminish or dilute the political efficacy of that group. Zimmer establishes certain subissues, the criteria, that a trial court must address before it can reach the ultimate issue of dilution. In essence, the criteria are directions that tell the trial court what type of circumstantial evidence can make out a dilution case. The court must address each subissue, if relevant to the particular case at hand,23 and determine whether the evidence under that criterion weighs in favor of or against a finding of dilution. The court is next to view the findings under the criteria as a whole, i. e., “in the aggregate,” Zimmer, 485 F.2d at 1305, giving due regard to the significance and strength of the finding under each subissue, to determine if the ultimate inference of dilution is permissible, and, if so, whether the evidence preponderates in its favor. See Blacks United for Lasting Leadership, Inc. v. City of Shreveport, 571 F.2d at 251. “The process does not differ from that of inferring ultimate facts from basic facts in other areas of the law. It is grounded in an experiential, intuitive assessment of the likelihood that the decision was designed to further one or another objective.” Brest, Palmer v. Thompson: An Approach to the Problem of Unconstitutional Legislative Motive, 1971 Sup.Ct.Rev. 95,121. We think that the district court in this case properly followed the mandate of Zimmer and correctly applied its test, and we turn to the findings of the district court that appellants question here.
The district court held on remand that there had been no showing of lack of black access to the electoral processes in Fairfield. The court’s earlier opinion noted that in 1968 six blacks won election to the council24 but that in 1972 blacks failed to win any of the eight seats they contested. The court attributed the marked disparity in these results not to any invidious racial discrimination but rather to .the failure of blacks to *227turn out a higher percentage in 1972.25 The testimony of one of the witnesses was cited as “quite candid ... in saying that there was no difficulty in qualifying to run for the city council.” The witness went on to characterize the task facing a candidate as “essentially ... a matter of getting out the vote, of getting more votes than the opponent or opponents did.”
Given these findings, which our prior panel found to be valid, we cannot rule the district court’s conclusion of accessibility clearly erroneous. The success or failure of black candidates appears to depend not upon any barriers to access to the slating or registration stages of Fairfield’s political processes but upon racially polarized voting in an at-large setting and the shifting racial makeup of the voting population.
The district court’s opinion on remand states that the appellants have not demonstrated unresponsiveness by city officials to the needs of black residents. The original opinion contains findings that “blacks have gotten far more responsiveness from city council when there were blacks on the city council.” The court also noted, however, “that blacks have not had the door completely closed in their faces insofar as expressing their opinions at city council meetings, in seeking assistance, presenting petitions, being heard, and on some occasions being given what amounts to private audiences for the presentation of these matters.” And finally, “the court has sensed that some of these requests have gotten answers, not to the same degree that the witnesses or that the black communities as a whole wanted, but there has not been a total lack of responsiveness merely because there were no blacks on the city council.” The panel on first appeal found the district court’s determination not to be clearly erroneous, and the finding on remand of sufficient responsiveness on the part of the city council is consistent with that determination. Therefore, the finding must stand.
The final factual determination challenged by the appellants is the district court’s conclusion that “plaintiffs have not proved that past discrimination precludes the effective participation by blacks in the election system.” The parties did not introduce evidence concerning the existence of racial motivation in the passage of the original, 1909 version of the districting legislation. Furthermore, as noted, the appellants failed to supply the court with any substantial evidence of past discrimination relating to Fairfield’s electoral system. Since the appellants clearly had the burden of coming forward with evidence of past racial discrimination that precludes the effective participation of blacks in the electoral process today,26 McGill v. Gadsden County Commission, 535 F.2d 277, 280 (5th Cir. 1976), the district court’s conclusion in its more recent opinion that such preclusion has not been shown to exist must stand as well.
We note that not all the district court’s findings under Zimmer have been challenged in this appeal. The appellees do not challenge the finding that the state policy behind at-large districting is tenuous, nor do they dispute the district court’s findings under the enhancing factors: that the district is large; that a majority vote require*228ment exists, but that since only two candidates run for virtually all positions, the requirement is “for all practical purposes no different from a plurality vote requirement”; and that the Fairfield plan requires candidates to run for numbered positions. Nor do the appellants challenge the finding that there is a residency requirement in Fairfield’s plan. Since these findings have not been disputed, they are not open to question on appeal.
We find the district court’s factual determinations under Zimmer not clearly erroneous; therefore, the only primary factor that we take to be established in the appellants’ favor is the existence of a tenuous state policy behind at-large districting. The district court found this showing, “[e]ven when ‘enhanced’ by two or possibly three of the ‘extra’ factors,” to be “insufficient ‘in the aggregate’ to establish a case of ‘dilution.’ ” Consequently, our only remaining task is to determine whether this conclusion is correct as a matter of law.
IV. The District Court’s Interpretation of Zimmer and Subsequent Dilution Precedents
The final issue we must address is whether the district court’s conclusion that dilution had not been demonstrated represents a proper interpretation of Zimmer and other applicable case law. We note initially that the district court properly followed the instructions in our prior opinion in this case to base its conclusions “on the criteria that . Zimmer . . . distilled from White v. Regester . . . and in accordance with all later cases.” 533 F.2d at 1365. The district court has made specific findings with regard to each of the dilution criteria.
We find also that the court properly approached the task of weighing the Zimmer factors. As we have stated, the task before the district court is to determine whether the criteria in the aggregate indicate a racially motivated dilution. The district court correctly performed its task when it proceeded from the understanding that “ ‘dilution’ is to be defined as the ‘aggregate’ of the factors outlined in Zimmer, bearing in mind that ‘all of these factors need not be proved in order to obtain relief.’ ” Furthermore, after concluding that of the primary factors, the appellants had established only the existence of a tenuous state policy, the court held this showing to be “insufficient ‘in the aggregate’ under [the Zimmer ] criteria to establish a case of dilution.’ ”
We find the district court’s conclusion wholly correct. We cannot say that a finding of a tenuous state policy behind at-large districting, standing alone, makes out a case under Zimmer or any other controlling precedent. In the absence of other evidence indicating the existence of intentional discrimination, state enactments providing for at-large districting are entitled to the deference afforded any other statute: their means need only be reasonably related to ends properly within state cognizance. E. g., Ohio Bureau of Employment Services v. Hodory, 431 U.S. 471, 97 S.Ct. 1898, 1910, 52 L.Ed.2d 513 (1977); F. S. Royster Guano Co. v. Virginia, 253 U.S. 412, 415, 40 S.Ct. 560, 64 L.Ed. 989 (1920); Lindsley v. Natural Carbonic Gas Co., 220 U.S. 61, 78-79, 31 S.Ct. 337, 55 L.Ed. 369 (1911). That these minimal constraints are satisfied by state statutes providing for government by representatives elected at-large is beyond dispute. The Supreme Court and this circuit have repeatedly rejected contentions that at-large districting is per se unconstitutional. E. g., White v. Regester, 412 U.S. at 765, 93 S.Ct. 2332; Whitcomb v. Chavis, 403 U.S. at 142, 91 S.Ct. 1858; Lipscomb v. Wise, 551 F.2d 1043, 1046 (5th Cir. 1977), cert. granted, - U.S. -, 98 S.Ct. 716, 54 L.Ed.2d 750 (1978); Turner v. McKeithen, 490 F.2d 191, 196 n. 23 (5th Cir. 1973); Zimmer, 485 F.2d at 1304.
The question whether the enhancing factors found to exist are sufficient in this case, when aggregated with the existence of a tenuous state policy, is a factual issue that must be resolved by the district court. Given the inability of the appellants to establish any additional criteria that would lend support to an inference of racially mo*229tivated dilution, the trial court’s determination must stand.
The appellants did not demonstrate a lack of access to the political processes in Fair-field. They did not establish that the commission was unresponsive to the needs of the black community, and although this failure does not preclude a finding of dilution, McGill v. Gadsden County Commission, 535 F.2d 277, 280 n. 7 (5th Cir. 1976); Zimmer, 485 F.2d at 1306-07 n. 6, it weighs heavily against an inference of intentional discrimination because the incumbents are not visibly exploiting their majority status to the detriment of the minority constituents. No residual effects of past discrimination were found to preclude the effective political participation of blacks in Fairfield. Indeed, six blacks were elected to the city council in 1968, and the district court found the failure of black candidates in 1972 to be due not to invidious racial discrimination but to a failure to turn out more of the black vote.
Under these particular circumstances, the district court’s conclusion that “there has been no evidence that the claimed ‘dilution’ was the result of any invidious discriminatory purpose” (citing Davis) is wholly warranted. The failure to establish the existence of intentional discrimination follows naturally from the factual determinations under Zimmer in this case.
This case, then, falls squarely within the principle established in Wright and reaffirmed in Davis and Arlington Heights. In the aggregate, the Zimmer criteria do not point to a racially motivated dilution. Absent a showing that intentional discrimination was a motivating factor in either the enactment or maintenance of the plan, these appellants cannot succeed.
The district court’s judgment is therefore
AFFIRMED.
APPENDIX
The Opinion of the District Court
MEMORANDUM OF OPINION
This court, under the mandate received June 10, 1976, is to reconsider its earlier decision in the light of the principles stated in the opinion of the Court of Appeals. Due to imminent deadlines for compliance with election law procedures, oral argument was, with consent of the parties, immediately scheduled. This memorandum supplements (and, to the extent inconsistent, supersedes) the earlier findings and conclusions of the court, which will not be repeated.
The first task is to make specific findings with respect to the four principal factors outlined in Zimmer v. McKeithen, 485 F.2d 1297, 1305 (CA5 1973), as the criteria for determining “dilution”.
(1) The plaintiffs, blacks residing in the City of Fairfield, have not demonstrated any lack of access to the process of slating candidates for city elections; for in Fairfield there has been no such slating. Perhaps more to the point, the evidence has not shown that blacks in recent years have been denied access to participation in any parts or phases of the election processes in Fairfield, e. g., qualifying as candidates, campaigning, voting.
(2) It has not been demonstrated that there has been “unresponsiveness” by city officials to the “particularized needs” of blacks. This is not, of course, merely a question of whether the city officials have listened to, and given some answer to, the special requests of the black citizens of the city. Nor is it a question of whether those officials have always complied with those requests. Rather, the standard involves an inquiry into whether the officials have reacted to those needs with sympathy and concern — such as would be expected of persons holding a public trust for all the citizenry of a community, who are ultimately accountable to all the voters at the next election. While the evidence has shown that blacks have fared less well during an all-white city administration than during a racially-mixed administration or than under the laws of chance, it has not established “unresponsiveness” under this standard. In this respect, it should be noted that the inquiry is directed to “unresponsiveness ”, *230referring to a state, condition or quality of being unresponsive, and is not established by isolated acts of being unresponsive.
(3) Under state law, cities of the size of Fairfield are permitted to divide the city into wards and to decide upon the number of such wards. If more than seven wards are created, then each ward, by vote of the ward, will elect a single member to the city council (with the president of the council, and perhaps other members being elected from the city at-large). If less than eight wards are created, then all members of the council will be elected by at-large vote, with two members being resident of each ward. In view of this optional dichotomy, it cannot be said that there is a state policy favoring at-large or multi-member districts for city council in preference to single-member ward-elected districts. (Proof that there is no such state policy should suffice to establish that any such state policy is “tenuous”.)
(4) The plaintiffs have not proved that past discrimination precludes the effective participation by blacks in the election system. The discrimination made known to the court pre-dated the elections in 1968, in which six of the 13 persons elected to the council were black. The failure to elect any blacks to the thirteen member council in 1972 was not the result of past discrimination, but rather the consequence of (a) a failure to turn out a higher percentage of black voters than of white voters, (b) bloc voting, and (c) at-large voting for numbered places.
Next, the court is to make specific findings on the “enhancing factors” outlined in Zimmer v. McKeithen, supra, 485 F.2d at 1305.
(1) Since the past elections have been from the city at large, the election district must be considered “large”, at least in a relative sense. The district is as large as it can be.
(2) There is a majority vote requirement. Where, however, as in the 1972 election, there are but two people running for virtually all positions, a majority vote requirement is for practical purposes no different from a plurality vote requirement.
(3) There is no anti-single shot voting provision since candidates run for numbered positions. The numbered position approach does' have some of the same consequences however as an anti-single shot, multi-member race; because a cohesive minority is unable to concentrate its votes on a single candidate. The numbered position approach does, however, eliminate the problem caused when a minority group is unable to field enough candidates in anti-single shot, multi-member races.
(4) There is a provision, a requirement, that the at-large candidates for the city council (excecting the position of President) be residents of particular geographical subdistricts.
When this court entered its earlier decision, it did so in the belief that “dilution” was established upon proof that (a) in a city where blacks constituted a majority of the voters in some of the districts but slightly less than 50% of the voters for the city as a whole, (b) where voting rather strictly followed racial lines, (c) a “winner-take-all” election system by at-large voting for numbered places resulted in practice (d) in an all-white governing body, (e) whose decisions, though without indication of fraud or bad faith, quite understandably tended to reflect their own perspectives and the attitudes of those who elected them, to the relative detriment of the black minority, (f) including such matters as appointments to other boards and agencies of the city. The court was of the view that such evidence demonstrated that the black plaintiffs “had less opportunity than did other residents in the district to participate in the political processes and to elect legislators of their choice.” White v. Regester, 412 U.S. 755, 766, 93 S.Ct. 2332, 2339, 37 L.Ed.2d 314 (1973). The court thought that the factors outlined in Zimmer were to be taken as indicia of — but not necessarily the determinants of — “dilution”.
*231The court now understands that its approach was in error and that “dilution” is to be defined as the “aggregate” of the factors outlined in Zimmer, bearing in mind that “all of these factors need not be proved in order to obtain relief.” 485 F.2d at 1305. It appears that only one of the four primary factors — number (3) — has been established by plaintiffs. Factors (1) and (4) have clearly not been proved. The evidence respecting factor (2) is mixed, but, using what the court believes to be the appropriate meaning of “unresponsiveness”, this factor has likewise not been proved to the court’s reasonable satisfaction.
Even when “enhanced” by two or possibly three of the “extra” factors, proof of factor (3) is insufficient “in the aggregate” under these criteria to establish a case of “dilution.” Accordingly, the court finds and concludes that there has not been proved an impermissible dilution of black votes under the existing Fairfield system. It may be noted that there has been no evidence that the claimed “dilution” was the result of any invidious discriminatory purpose. Cf. Washington v. Davis, 426 U.S. 229, 96 S.Ct. 2040, 48 L.Ed.2d 597 (1976).
Judgment in favor of the defendants will be entered by separate order.
This the 11th day of June, 1976.
/s/ Sam C. Pointer. Jr.
United States District
Judge
. The other cases are Bolden v. City of Mobile, 571 F.2d 238 (5th Cir. 1978); Blacks United for Lasting Leadership, Inc. v. City of Shreveport, 571 F.2d 248 (5th Cir. 1978); Thomasville Branch of the NAACP v. Thomas County, 571 F.2d 257 (5th Cir. 1978).
. This case is before us for the second time. The first panel reversed and remanded the district court’s judgment for the black residents. Nevett v. Sides, 533 F.2d 1361 (5th Cir. 1976). On remand, the district court rendered judgment in favor of the city, and the black residents took this appeal.
. These plaintiffs brought suit under the authority of 42 U.S.C. §§ 1981 and 1983 (1970). Record, vol. 1, at 1. They allege no additional statutory violations. Therefore, this case does not present the issue, discussed at length in Judge Wisdom’s special concurrence, whether Congress intended in the Voting Rights Act to go beyond the protection provided by the Constitution and invalidate at-large voting schemes, like that of Fairfield, that are not illicitly motivated. See part II infra.
. The applicable statute is Ala.Code tit. 37, § 426 (Supp.1973). It has remained substantially unchanged, except for the specific population categories, since its original enactment in 1909. Section 426 provides as follows:
Election of president of council and aider-men. — In cities having a population of twelve thousand or more, there shall be elected at each general municipal election the following officers, who shall compose the city council for such cities, and who shall hold office for four years and until their successors are elected and qualified, and who shall exercise the legislative functions of city government and any other powers and duties which are or may be vested by law in the city council or its members: A president of the city council, and in cities having seven wards or less, two aldermen from each ward, to be elected by the qualified voters of the several wards voting separately in every ward, except in cities of léss than twenty thousand population, in which two aldermen from each ward shall be elected by the electors of the city at large, in cities having more than seven wards, one alderman from each ward, and a sufficient number of aldermen from the city at large to make the total number of aldermen fourteen exclusive of the president of the council, and in cities having fifty thousand population or more the city council may create not exceeding twenty wards. The president of the council shall have the right to vote on all questions the same as any other member of the council Provided however, that the city council of any city having a population of twelve thousand or more may by ordinance or resolution, if adopted by two-thirds vote of the city council more than six months prior to any general municipal election, provide that the city council of said city shall consist of five aldermen to be elected from the city at large. And provided further, that the city council of any city having a population of more than thirty thousand, according to the last or any subsequent federal decennial census, or according to any census of such city made pursuant to article 3 of chapter 10 of this title, or Act No. 845 of the Acts of 1953 (sections 481(1) and 481(2) of this title,) and having only five wards, may, by ordinance or *214resolution adopted by two-thirds vote of the city council, at least six months prior to a general municipal election, provide that the city council shall consist of a president and five aldermen. If such an ordinance or resolution is adopted one alderman shall reside in each of the respective wards of the city, the president and all the aldermen shall be elected by the voters of the city at large, and the president shall vote only in case of a tie.
. Neither the record nor the briefs indicate when Fairfield opted to section itself into six wards. The state statute granting municipalities the option of determining the number of wards was originally enacted in 1909. 1909 Ala.Acts 100. Since neither appellants nor appellees emphasized the issue of when Fairfield exercised its option, we will assume that at all times relevant to this appeal Fairfield had six wards and elected its aldermen at-large.
. Population figures are not available for the election years 1968 and 1972. In 1970, the year of the decennial census, blacks constituted 48% of Fairfield population but at least 50% of its registered voters. See Nevett v. Sides, 533 F.2d 1361, 1365 n. 3 (5th Cir. 1976).
. The district court’s original findings of fact and conclusions of law are reported as appendices to our prior opinion, Nevett v. Sides, 533 F.2d 1361, 1366-76 (5th Cir. 1976).
. The Supreme Court affirmed, “but without approval of the constitutional views expressed by the Court of Appeals.” 424 U.S. at 636, 96 S.Ct. at 1085. Notwithstanding, Zimmer continues to control dilution cases in this circuit. Blacks United for Lasting Leadership, Inc. v. City of Shreveport, 571 F.2d 248, 251-252 (5th Cir. 1978).
. The district court’s opinion on remand is set forth in full in the appendix to this opinion.
. A provision requiring that each elector cast votes for as many candidates as there are positions is known as an anti-single shot rule. An anti-single shot rule has application only in the context of an electoral scheme that selects winners by ranking all candidates in the order of the number of votes they receive. If there are x offices, the top x candidates fill them. This electoral scheme is denominated the “single-ballot-plurality” voting system. See R. Dixon, Democratic Representation: Reapportionment in Law and Politics 505 (1968); Silva, Relation of Representation and the Party System to the Number of Seats Apportioned to a Legislative District, 17 W.Pol.Q. 742 (1964). An anti-single shot rule invalidates all ballots that do not show votes for as many candidates as there are positions. Minority voters can be disadvantaged by such a rule because it may force them to vote for nonminority candidates, thus depreciating the relative position of minority candidates.
The numbered position provision in force in Fairfield, also known as a “place” rule, requires candidates to choose one of a given number of positions and run for it. Thus, given x positions, it is as if there were x separate district-wide contests. The place system disadvantages minorities by causing minority candidates to run in head-to-head contests against majority candidates. See White v. Regester, 412 U.S. 755, 766, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973).
. Since the four cases we decide today allege dilution of black votes, our holdings are necessarily limited to cases entertaining claims of racial discrimination.
. That a districting scheme is motivated by racial considerations does not necessarily render it subject to invalidation under the equal protection clause. A districting body may properly consider race if the plan does not “slur or stigmaftize]” any race and does not “fence out” a racial group from participation in political processes or “minimize or unfairly cancel out” such a group’s voting strength. *219United Jewish Organizations v. Carey, 430 U.S. 144, 165, 97 S.Ct. 996, 1009, 51 L.Ed.2d 229 (1977). Although a benign plan, which is designed to remedy the underrepresentation of a racial minority group, is permissible under the Constitution, a state or locality is under no obligation to provide minorities, racial or otherwise, with representation proportionate to their voting power. E. g., White v. Regester, 412 U.S. 755, 765-66, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973); Whitcomb v. Chavis, 403 U.S. 124, 152, 91 S.Ct. 1858, 29 L.Ed.2d 363 (1971).
. Appellants point out, however, that neither Davis nor Arlington Heights contains any reference to voting dilution decisions such as Regester, Chavis, and Zimmer. These dilution cases, appellants contend, have not.required a showing of intentional racial discrimination, and hence the failure of Davis or Arlington Heights expressly to overrule these dilution precedents indicates they are an exception to the general rule.
Appellants’ error is that they misconceive these dilution precedents. Regester and Zimmer do not hold that a showing of intent is unnecessary for a finding of unconstitutional dilution. Racially motivated discrimination was a significant factor in both Regester and Zimmer. In Regester, the Court found a “history of official racial discrimination . . ., which at times touched the right of Negroes to register and vote and to participate in the democratic process,” 412 U.S. at 766, 93 S.Ct. at 2339, and in Zimmer, the Court noted that “minority residents . . . have suffered from a protracted history of racial discrimination which touched their ability to participate in the electoral process.” 485 F.2d at 1306.
We recognize that neither Regester nor Zimmer dealt with the issue of racially motivated discrimination in the enactment of the at-large plans contested in those cases. The necessary intent, however, need not exist at the passage of the plan. All that is necessary is that the invidiously disproportionate impact “ultimately *220be traced to a racially discriminatory purpose.” Davis, 426 U.S. at 240, 96 S.Ct. at 2048. Thus, as we recently held in Kirksey, a plan, pristine in its enactment, that carries forward past discrimination is violative of the fourteenth amendment. Similarly, a plan legitimate at its inception may become a vehicle for intentional discrimination and hence become unconstitutional when changing circumstances render it invidiously discriminatory. Bolden v. City of Mobile, 571 F.2d 238 (5th Cir. 1978).
. The fifteenth amendment was ratified in , 1870, but was not successfully invoked before the Supreme Court until 1915, when the Court nullified an Oklahoma provision exempting those who were qualified to vote prior to 1868 and their descendants from literacy and property requirements. Guinn v. United States, 238 U.S. 347, 35 S.Ct. 926, 59 L.Ed. 1340 (1915); accord, Myers v. Anderson, 238 U.S. 368, 35 S.Ct. 932, 59 L.Ed. 1349 (1915). Since blacks were disenfranchised prior to the adoption of the amendment, this “grandfather clause” required blacks to pass literacy and property tests while exempting whites. When the Oklahoma legislature substituted a provision preserving the registrations of all those who had qualified under the invalidated provisions but requiring others to register within a given eleven-day period (or lose eligibility forever), the Supreme Court invalidated the substitute. Lane v. Wilson, 307 U.S. 268, 59 S.Ct. 872, 83 L.Ed. 1281 (1939). Subsequent decisions under the fifteenth amendment invalidated attempts to exclude blacks from party nominating processes, Terry v. Adams, 345 U.S. 461, 73 S.Ct. 809, 97 L.Ed. 1152 (1953); Smith v. Allwright, 321 U.S. 649, 64 S.Ct. 757, 88 L.Ed. 987 (1944), and invidiously to administer literacy tests, Louisiana v. United States, 380 U.S. 145, 85 S.Ct. 817, 13 L.Ed.2d 709 (1965); Davis v. Schneli, 81 F.Supp. 872 (S.D.Ala.), affd, 336 U.S. 933, 69 S.Ct. 749, 93 L.Ed. 1093 (1949).
Gomillion v. Lightfoot, 364 U.S. 339, 81 S.Ct. 125, 5 L.Ed.2d 110 (1960), is the first reapportionment case decided under the amendment. It, of course, held that a complaint alleging a racial gerrymander states a cause of action under the fifteenth amendment. See also Wright v. Rockefeller, 376 U.S. 52, 84 S.Ct. 603, 11 L.Ed.2d 512 (1964); Smith v. Paris, 257 F.Supp. 901 (M.D.Ala.1966), aff’d per curiam, 386 F.2d 979 (5th Cir. 1967); Sims v. Baggett, 247 F.Supp. 96 (M.D.Ala.1965). For a more detailed discussion of the history and development of the fifteenth amendment, see W. Gillette, The Right to Vote: Politics of the Passage of the Fifteenth Amendment (1965); J. Matthews, Legislative and Judicial History of the Fifteenth Amendment (1909); Lucas, Dragon in the Thicket: A Perusal of Gomillion v. Lightfoot, 1961 Sup.Ct.Rev. 194.
. See discussion, supra note 14.
. If racially polarized voting did not exist, white candidates could not expect to retain or achieve office solely because they were white. Their black constituents would constitute merely another minority group that might become an element necessary to the formation of a majority coalition. Under these conditions, white officeholders would ignore black needs at their peril.
Additionally, in the absence of polarized voting, black candidates could not be denied office because they were black, and a case of unconstitutional dilution could not be made. “[I]f voting does not follow racial lines, the [voter of the minority race] has little reason to complain . . . .” United Jewish Organization v. Carey, 430 U.S. 144, 166 n. 24, 97 S.Ct. 996, 1010, 51 L.Ed.2d 229 (1977).
. As the Supreme Court has recently noted, “there is no authority for the proposition that the candidates who are found racially unacceptable by the majority, and the minority voters supporting those candidates, have had their Fourteenth or Fifteenth Amendment rights infringed by this process.” United Jewish Organizations v. Carey, 430 U.S. 144, 167, 97 S.Ct. 996, 1010, 51 L.Ed.2d 229 (1977); accord, Nevett v. Sides, 533 F.2d 1361, 1365 (5th Cir. 1976).
. Bloc voting may be indicated by a showing under Zimmer of the “existence of past discrimination in general .... large districts, majority vote requirements, anti-single shot voting provisions and the lack of provision for at-large candidates running from particular geographical subdistricts.” 485 F.2d at 1305. Of course, bloc voting may be demonstrated by more direct means as well, such as statistical analyses, e. g., Bolden v. City of Mobile, 423 F.Supp. 384, 388-89 (S.D.Ala. 1976), aff’d, 571 F.2d 238 (5th Cir. 1978), or the consistent lack of success of qualified black candidates.
. Showings of unresponsiveness and lack of access make a strong dilution case. The capacity of a governing body to respond to the needs of its constituency is, in large measure, what makes that body representative. See H. Pitkin, The Concept of Representation 233 (1972). Ideally, electoral processes are designed to provide an institutional and periodic method of guaranteeing governmental responsiveness. “Our concern with elections and electoral machinery, and particularly with whether elections are free and genuine, results from our conviction that such machinery is necessary to insure systematic responsiveness.” Id. at 234.
Thus, if representatives are unresponsive to the needs of a racial group apparently because some stages of the electoral process diminish the group’s input, the inference that the processes are maintained with the purpose to discriminate can fairly be drawn.
[At-large] districts, it would seem, violate the Equal Protection Clause, not because they overrepresent or underrepresent pure and simple, but because they do that in a context where all stages of the electoral processes have been effectively closed to identifiable classes of citizens, making the political establishment ‘insufficiently responsive’ to [those classes] interests.
Casper, Apportionment and the Right to Vote: Standards of Judicial Scrutiny, 1973 Sup.Ct. *224Rev. 1, 28. See also Hendrix v. Joseph, 559 F.2d 1265, 1269 (5th Cir. 1977).
. Professor Brest summarizes the relevance of the weight of the state policy as follows:
The courts possess no general authority to invalidate a decision because it is “undesirable,” and an allegation of illicit motivation does not enlarge their authority. A conscientious decisionmaker, however, considers the costs of a proposal, its conduciveness to the ends sought to be attained, and the availability of alternatives less costly to the community as a whole or to a particular segment of the community. That a decision obviously fails to reflect these considerations with respect to any legitimate objective supports the inference that it was improperly motivated.
Brest, Palmer v. Thompson: An Approach to the Problem of Unconstitutional Legislative Motive, 1971 Sup.Ct.Rev. 95, 121-22.
. As we said recently in Kirksey v. Bd. of Supervisors, 554 F.2d 139 (5th Cir.) (en banc), cert. denied, - U.S. -, 98 S.Ct. 512, 54 L.Ed.2d 454 (1977), “[b]y proof of an aggregation of at least some of [the Zimmer] factors, or similar ones, a plaintiff can demonstrate that the members of the particular group in question are being denied access.” Id. at 143 (emphasis added).
. This procedure is not different from that employed by a fact finder in resolving any issue by circumstantial evidence. As in other circumstantial evidence cases, it may be that the findings in the plaintiffs’ favor, taken individually, cannot establish the ultimate issue. This does not necessarily foreclose relief. The aggregate of the evidence controls. “[T]he convergence of a number of decisions, each of which could be explained in terms of licit objectives . . . may support the conclusion that each of the decisions is illicitly motivated.” Brest, supra note 20, at 123 n. 139.
. As we note in Blacks United for Lasting Leadership, Inc. v. City of Shreveport, 571 F.2d 248, 255 n. 6, (5th Cir. 1978), dependent upon the nature of the scheme under attack, not all of the criteria may be relevant, and additional factors may have probative force. Notwithstanding, the multifactor test established in Zimmer is the touchstone in dilution cases, and the trial judge must look to it for guidance in determining what subissues may be appropriate.
. Seven black candidates qualified to run for city council in 1968. All but the candidate for council president prevailed.
. As the district court stated in its opinion on remand, “[t]he failure to elect any blacks to the thirteen member council in 1972 was not the result of past -discrimination, but rather the consequence of (a) a failure to turn out a higher percentage of black voters than of white voters, (b) bloc voting, and (c) at-large voting for numbered places.”
. We are fully aware of the recent holding in Kirksey v. Bd. of Supervisors, 554 F.2d 139 (5th Cir. 1977) (en banc), cert. denied, - U.S. -, 98 S.Ct. 512, 54 L.Ed.2d 454 (1977), that required the defendants in that case to bear the burden of coming “forward with evidence that enough of the incidents of the past had been removed, and the effects of past denial of access dissipated, that there was presently equality of access.” Id. at 144-45. The reasoning leading to the placement of this burden on defendants is not apposite in this case. The en banc court emphasized that the plaintiffs had demonstrated “sweeping and pervasive” past intentional discrimination. Id. at 144. Furthermore, the intentional discrimination was shown to have continued to within a few years of the present. In this case, however, the appellants have not demonstrated pervasive discrimination in Fairfield’s electoral processes in the past, remote or recent.