Plaintiff appeals from a district court approved plan of reapportionment for the Winn Parish School Board and Winn Parish Police Jury. Plaintiff argues that the apportionment of the School Board violates the “one man-one vote” maxim of Reynolds v. Sims, 377 U.S. 533, 84 S.Ct. 1362, 12 L.Ed.2d 506 (1964), and progeny in that the total variation between the highest represented and lowest represented district is 37.71%. Plaintiff also contends that the apportionment plan of the Police Jury, which utilizes both single and multi-member districts, results in a dilution of black votes in violation of the Fifteenth Amendment. In addition, plaintiff argues that the award of $500 attorney’s fees was excessively low.

I. School Board

Plaintiff below, attacked a 1970 court ordered apportionment of the School Board.1 That plan called for five election districts, with District 1 electing five at-large members, District 2 electing two at-large members with no more than one member from any one of the three wards constituting District 2, and Districts 3, 4, and 5 electing one member each for a total school board membership of ten persons. The district court, below, held that this 1970 plan did not offend Fourteenth Amendment “one man-one vote” requirements, but did violate the Fifteenth Amendment in its apportionment of District 1 into a five-person, multi-member district. Accordingly, the court approved a plan adopted by the school board that called for ten election districts, with District 1 divided into five single-member districts, with three other single-member districts, and with two voting districts combined to elect two members at-large.2

Plaintiff argues that the population variation of 37.71% between the most over-represented and the most underrepresented district is too great to withstand constitutional scrutiny. We agree. While mathematical exactitude is not required in state and local reapportionment plans, Reynolds v. Sims, supra, and while small variations from the ideal are insufficient to establish invidious discrimination, Gaffney v. Cummings, 412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973), a deviation of 37.71% is certainly beyond the de minimus range. In Swann v. Adams, 385 U.S. 440, 87 S.Ct. 569, 17 L.Ed.2d 501 (1967), the Supreme Court reversed a Florida legislative reapportionment plan that provided for a total variation from the ideal of 25% in the state senate and of 33% in the state house, basing its reversal on failure of the state or of the district court to articulate acceptable reasons for these substantial variations. Id. at 443-^44, 87 S.Ct. 569. Likewise, in Whitcomb v. Chavis, 403 U.S. 124, 91 S.Ct. 1858, 29 L.Ed.2d 363 (1971), the Court reversed a plan allowing total variations of 28% and 25% in each house of the Indiana legislature. Finally, in Kilgarlin v. Hill, 386 U.S. 120, 87 S.Ct. 820, 17 L.Ed.2d 771, reh. den., 386 U.S. 999, 87 S.Ct. 1300, 18 L.Ed.2d 352 (1967), the Court disapproved a 26% variation, noting that it was unsure that any policy considerations could justify such variations, although it did not have to reach that question since the plan did not achieve announced policy objectives.

In the present case, the district court did not articulate any reasons for allowing such a large variation among voting’districts. The defendants now argue that such deviations are required to *595achieve their objective of restricting school board election districts to traditional school attendance zones; that is, only voters within high school district 1 would vote for a school board member in the corresponding election district. Besides the fact that the approved plan does not even achieve this goal,3 we have recently held that such an objective cannot justify these significant variations. Panior v. Iberville Parish School Board, 498 F.2d 1232 (5th Cir. 1974). In Panior, the district court had approved a plan that created four school board election districts to conform to four high school sub-systems and that resulted in a 37.45% total variation among school board election districts. In reversing, we held:

The Board acts as a unit. The Board as a whole has the responsibility for operating all of the schools. The Board’s function and responsibility is not decentralized into the four segments. Granted that it is both understandable and permissible that election lines may be drawn to take into account centers of interest, this cannot justify deviations approaching those here for an election to an operative body which has to act as a unit. .

Each voter is, therefore, entitled, so far as practicable, to an equal voice in the ultimate responsibility for such action whether the brick and mortar are to go to East Bank or to Metropolitan Plaquemine. Whether any set of conceivable circumstances could justify a situation such as this where two voters in two districts all but equal three voters in two others, we simply hold this case falls far short of that mark. Id. at 1236. (Emphasis added.)

Accordingly, we reverse and remand that portion of the judgment setting up school board election districts and direct the district court to establish or approve a plan resulting in acceptable total variations in population among school board districts.

II. Police Jury

In the 1970 apportionment plan, the Police Jury was divided into two voting districts — districts A and B — with six representatives allotted to each district for a total Police Jury membership of twelve.4 The district court, below, holding that the apportionment of Ward A into a six multi-member district offended the requirements of the Fifteenth Amendment, adopted a plan proposed by the Police Jury that called for a ten member Police Jury with District A divided into five single-member districts (election districts one-five) and with District B maintained as a five person multi-member district (election districts six-ten).5 Plaintiffs challenge the retention of this “at-large” system of representation in Districts Six — Ten on Fifteenth Amendment grounds.6

It is difficult for us to determine from plaintiff’s brief, whether plaintiff argues that multi-member districts are per se unconstitutional or argues that the maintenance of District B (6-10) as a multi-member district unconstitutionally dilutes black votes. Certainly, multimember election districts are not per se unconstitutional. Kilgarlin v. Hill, 386 U.S. 120, 87 S.Ct. 820, 17 L.Ed.2d 771 (1967); Burns v. Richardson, 384 U.S. 73, 86 S.Ct. 1286, 16 L.Ed.2d 376 (1966); Fortson v. Dorsey, 379 U.S. 433, 85 S.Ct. 498, 13 L.Ed.2d 401 (1965). In analyzing the constitutionality of the use of such a scheme in the present case, we are cognizant that the Supreme Court has classified cases involving multi-member districts into two groups, with the classification dependent on whether the multimember election plan originated solely *596from the court or from a legislative body. In Chapman v. Meier, 420 U.S. 1, 95 S.Ct. 751, 42 L.Ed.2d 766 (1975), the Court held:

“[W]hen district courts are forced to fashion apportionment plans, single-member districts are preferable to large multi-member districts as a general matter.” [Connor v. Johnson, 402 U.S.] at 690, [91 S.Ct. 1760] 29 L.Ed.2d 268. . . .

The standards for evaluating the use of multimember districts thus clearly differ depending on whether a federal court or state legislature has initiated the use .

Appellants do not contend that any racial or political group has been discriminated against by the multimember districting order by the District Court. They only suggest that the District Court has not followed our mandate in Connor v. Johnson, and that the court has failed to articulate any reasons for this departure. We agree. Absent particularly pressing features calling for multimember districts, a United States district court should refrain from imposing them upon a State. Id. 95 S.Ct. at 761, 42 L.Ed.2d at 779-80.

Therefore, if this case were governed by Chapman, we would remand it back for failure of this district court to articulate compelling reasons for use of a multi-member plan. Consistent with our holding in Wallace v. House, 515 F.2d 619 (5th Cir. 1975), petition for cert. filed, 44 U.S.L.W. 3399 (U.S. Dec. 26, 1975) (No. 75 — 914), however, we do not believe the present case to be governed by Chapman, and, accordingly, we do not base our remand on the district court’s failure to articulate justifications for its plan. In Wallace, we held that when a district court, in invalidating an all at-large aldermanic election plan, is forced to formulate a new apportionment plan, it can properly choose the local legislative body’s proposed plan, utilizing some multi-member representation, rather than adopt a total single district plan, as long as that body’s plan is constitutional. Id. at 635-36. Interpreting the Supreme Court’s determinations in Connor and Chapman to be based on its supervisory powers over federal courts, as opposed to constitutional considerations, we distinguished these cases on the basis of the unusual facts operative in each of them: in Connor, the parties in the litigation had proposed plans utilizing single-member districts exclusively, but the district court, in its order reapportioning the Mississippi Legislature, had employed some multi-member districts; in Chapman, the use of multi-member ■ districts had originated solely from the district court and had never been proposed or sanctioned by the North Dakota legislature. L, Noting that in Wallace, unlike in the two Supreme Court cases, the impetus for a multi-member plan was derived from the governmental body in question, we held that “because of the complex political judgments involved in reapportionment plans,” courts could and should defer to legislative preferences when these preferences can result in constitutional plans.7 Id. at 636. Accordingly, since the local governmental body, and not the court, originated the multi-member plan in the present case and since there is some statutory history supporting such a plan,8 the district court did not contravene the mandate of Chapman in its adoption, without a showing of compelling justifications, of the Police Jury’s multi-member plan. The constitutionality of the present multi-district plan must still, however, be determined.

*597The Supreme Court has held that before a multi-member plan can be invalidated on constitutional grounds, it must be shown that “designedly or otherwise, a multi-member constituency 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.” Fortson v. Dorsey, 379 U.S. at 439, 85 S.Ct. at 501. Emphasizing that those invidious qualities which often characterize multi-member districts must be affirmatively demonstrated in the particular plan before it will be invalidated, the Court later stated:

We are not ready, however, to agree that multi-member districts, wherever they exist, overrepresent their voters as compared with voters in single-member districts, even if the multimember delegation tends to bloc voting. The theory that plural representation itself unduly enhances a district’s power and the influence of its vote remains to be demonstrated in practice and in the day-to-day operation of the legislature. Whitcomb v. Chavis, 403 U.S. 124 at 147, 91 S.Ct. 1858 at 1871, 29 L.Ed.2d 363.

Clearly, then, the burden of proving invidious discrimination through use of a multi-member system of districting is on the person challenging that plan.

Under the present plan, there are two possible ways in which dilution of political or racial elements could occur. First, one could argue that voters in District B (6-10) are benefited by the opportunity to elect their jury members in an at-large system, while those in District A (1 — 5) elect only a single member per district. According to this argument, each voter in District B votes for five police jury members; each voter in Ward A, divided into five districts, can vote for only one member. Therefore, with a total parish population of 16,360 —8,389 in Ward A and 7,971 in Ward B — it is conceivable that a given 4,000 voters in Ward B, over 50% of that Ward’s population but only 25% of the total parish population, could elect five members or 50% of the police jury. Each of those 4,000 voters in Ward B would thereby enjoy the voting power to elect five jury members, while each of the voters in Ward A would have the power to elect only one member. Such an argument is extremely speculative; indeed, plaintiff does not advance it here. Accordingly, while we believe that the combined single and multi-member system is extremely bizarre in the present case and seems to satisfy no particular state policy in favor of multimember districts, the fact that it is an illogical plan is not enough in itself to invalidate it. See, White v. Register, 412 U.S. 755 at 762, n.6, 93 S.Ct. 2332 at 2337, 37 L.Ed.2d 314 at 322 (1973) (fact that the use of single and multi-member districts might have constituted “irrational mixture” does not mean that the mere mixture of single and multi-member districts in a single plan, even among urban areas, is invidiously discriminatory). Kilgarlin v. Hill, 386 U.S. 120 at 121, 87 S.Ct. 820, 17 L.Ed.2d 771 (allegation that utilization of single-member, multi-member, and floterial districts constituted a “crazy quilt” did not prove racial or political gerrymander in violation of Fourteenth Amendment). Rather, if plaintiff wishes to attack the mixed single and multi-member districts, upon remand, on the basis of the above argument, he has the burden of proving that this scheme invidiously discriminates against identifiable racial or political elements.

A second possibility for dilution, under a Fifteenth Amendment theory, *598exists within District B itself. The district court reapportioned District A into five districts (Districts 1 — 5) because of Fifteenth Amendment considerations. From our examination of the briefs and statistics, we presume the court to have reasoned that blacks, who constituted 40.27% of District A, should have enjoyed the power to elect at least one of that Ward’s police jury members, but that because of the multi-member method of election, these black votes were diluted.9 Accordingly, the court divided A into five single-member districts that yielded one certain10 and one possible11 black seat. Likewise, there has been no black representation on the police jury from District B, a multi-member system under both the 1970 and 1974 plan. While District B contains only 19.3% black population, as opposed to the 40.27% figure for blacks in District A, it is still possible that a fairly drawn single-member plan, in B, as well as in A, could result in a greater and fairer role for black voters in police jury elections.

We cannot determine from the record whether the establishment of a single-member district in District B, as well as in District A, is necessary to avoid a dilution of black votes, in violation of the Fifteenth Amendment. We have examined the breakdown of residents in the School Board’s districts 6-10 — the Board equivalent of Police Jury District B. In these districts, the percentage of blacks in each district ranges from only 7% in District 6 to 39% in District 10.12 Therefore, one could argue that dividing District B into single-member districts would not significantly increase black participation in the jury election process, since it is doubtful that even 39%, much less 7%, of a district could “control” an election in that particular district. Yet, these population figures in Districts 6-10, showing a small percentage of blacks in each single-member district, are not dispositive in that we have already held that the substantial population variations among school districts violate the Fourteenth Amendment. In addition, the greatest variation between school board districts occurs between District 7/8, with 20% overrepresentation, and District 10, with 18% underrepresentation— both of which are located in District B. Accordingly, School Board Districts 6-10 are severely malapportioned and must be redistricted before we can determine whether a similar single-member scheme for police jury elections is necessary to avoid dilution of black votes.

From our examination of the maps in the record, we also note that School Board District 10, with a 39% black population, is adjacent to District 9 (19% black population) and District 5 (27% black population). When the district court redraws the school board lines, it is possible that the black population may be significant enough in one or more districts to compel total single-member districting for police jury elections.

Accordingly, we remand the apportionment plan for the police jury to the district court in order that it might redraw school board single-member districts, and might then compare, for the purpose of adopting a plan for police jury elections, the impact on black voters of a properly apportioned single-member district system with that of a multi-member plan.

In addition to raw population data, the district court should examine those other factors that have been established to aid courts in their analysis of multi-member plans. In Zimmer v. McKeithen, 485 F.2d 1297 (1973), we noted some of those considerations when we held:

[W]here a minority can demonstrate a lack of access to the process of slating candidates, the unresponsiveness of *599legislators to their particularized interests, a tenuous state policy underlying the preference for multi-member or at-large districting, or that the existence of a past discrimination in general precludes the effective participation in the election system, a strong case is made. Such proof is enhanced by a showing of the existence of large districts, majority vote requirements, anti-single shot voting provisions and the lack of provision for at-large candidates running from particular geographical subdistricts. The fact of dilution is established upon proof of the existence of an aggregate of these factors. [Footnotes omitted.] Id. at 1305.

We note that many of the factors that tend to invalidate multi-member schemes —a majority vote requirement, an anti-single shot voting provision, and the absence of a requirement that at-large candidates run from a specified geographic area — exist here and we direct the court to carefully weigh their effect before it imposes any multi-member plan for the police jury.

III. Attorney’s Fees

Plaintiff argues that the district court’s award of $500.00 in attorney’s fees was unduly low. While we agree that the trial court acted properly in awarding some attorney’s fees,13 we disagree that the amount awarded was erroneous. This court has consistently held that the determination of a reasonable attorney’s fee is left to the sound discretion of the trial judge and is not to be set aside absent a clear abuse of that discretion. E. g., Ranger Ins. Co. v. Algie, 482 F.2d 861 (5 Cir. 1973); Weeks v. So. Bell Tel. & Tel. Co., 467 F.2d 95 (5th Cir. 1972); Electronics Capitol Corp. v. Sheperd, 439 F.2d 692 (5th Cir. 1971). Plaintiff does not set out any particular reasons to justify his argument that the trial court’s award constituted an abuse of discretion. He merely cites two election cases in which attorneys received a higher award for his proposition that the present award was too low. After examination of the record in the present cáse, we cannot say that the trial court’s award constituted a clear abuse of discretion.

Affirmed in part — reversed in part. Appendix to follow.

*600APPENDIX I

WINN PARISH SCHOOL BOARD

1974 COURT-ORDERED PLAN

Voting Black District Members Population Population % Black 1970 District > Variation Plan

1 1 1639 1639 100 + .18 1

2 1 1693 465 27 + 3.14 1

3 1 1678 816 45 + 2.57 1

4 1 1688 0 0 + 3.17 1

5 1 1691 458 27 + 3.36 1

6 1 1819 125 7 +11.19 5

7/s 2 2627 374 14 -19.68 2

9 1 1594 295 19 -2.57 4

10 _1 1931 744 _39 +18.03 3

TOTAL 10 16,360 4916 30 37.71

1970 School Board Plan, ordered in Sanders v. Winn Parish School Bd. was same as above, except districts 1-5 of the present plan were consolidated into one five person multi-member district and districts 6-10 were numbered districts 2-5 (see column 7 above).

APPENDIX II

WINN PARISH POLICE JURY

1974 COURT-ORDERED PLAN

Voting Number of Black District Representatives Population Population % Black % Variation

1 1639 1639 100 + .18

2 1693 465 27 + 3.48

3 1678 816 45 + 2.57

4 1688 0 0 + 3.17

_5 1691 458 27 + 3.36

TOTAL 8389 3378 40.27 **

6-10* 7971 1538 19.29 -2.57

1970 COURT-ORDERED PLAN IN ALLEN v. WINN PARISH POLICE JURY

A * 6 8389 40.27

B ** _6 7971 19.29

TOTAL 12 16,360