BAUER, Circuit Judge.
Defendants appeal from the district court order requiring them to increase the size of the Board of Commissioners of Cook County (“Board”) from fifteen members, nine elected from Chicago and six from the suburbs, to seventeen members, ten elected from Chicago and seven from the suburbs. Defendants contend that the district court erred in ordering reapportionment because the plaintiffs failed to prove that the Board’s fifteen member apportionment plan diluted their voting rights in violation of the fourteenth amendment. We affirm.
I
Plaintiffs originally filed this reapportionment suit in 1973. They alleged that the Board, which then had fifteen members, ten elected from Chicago and five elected from the suburbs, overrepresented Chicago citizens by 4.87% and underrepresented suburban citizens by 4.87%. The district court held that the 9.74% total deviation diluted the voting rights of the suburban voters in violation of the fourteenth amendment. The court ordered the Board to increase its size to sixteen members, ten to be elected from the city and six from the suburbs. The court’s reapportionment plan decreased the total deviation to 1.4%, the smallest feasible deviation. Sutton v. Dunne, 365 F.Supp. 483 (N.D.Ill.1973). Defendants did not appeal the district court’s 1973 reapportionment order.
On October 15, 1973, the Board adopted an ordinance implementing the district court’s reapportionment plan. The 1974 and 1978 Board elections were held on the basis of that ordinance. On November 2, 1981, the Board passed an ordinance decreasing its size to fifteen members, nine to [486]*486be elected from the city and six from the suburbs. The Board’s 1981 apportionment plan was based on Cook County population figures from the 1980 census.
Plaintiffs returned to the district court to obtain modification of the court’s 1973 order to reflect 1980 population changes. Plaintiffs requested the court to reject the Board’s 1981 plan and order it to increase either to sixteen members, nine to be elected from the city and seven from the suburbs, or to seventeen members, ten to be elected from the city and seven from the suburbs. Using adjusted raw population figures from the 1980 census,1 the district court calculated that the Board’s 1981 plan created a 2.11% overrepresentation of Chicago citizens and a concomitant 2.11% un-derrepresentation of suburban citizens. The court held that the plan’s 4.22% total deviation violated the fourteenth amendment. The court also rejected the plaintiffs’ plan calling for a proposed sixteen member Board because that plan created an unacceptable 3.28% total deviation, with Chicago underrepresented by 1.64% and the suburbs overrepresented by a like amount. The court adopted the plaintiffs’ alternate plan and ordered the Board to increase its size to seventeen members, ten to be elected from Chicago and seven from the suburbs. The court found that this apportionment plan would result in a .93% underrepresen-tation of the suburbs and .93% overrepre-sentation of the city voters, with a total deviation of 1.86%. Sutton v. Dunne, 529 F.Supp. 312 (N.D.I11.1981).
II
Defendants claim that the district court erred in ordering them to adopt plaintiffs’ apportionment plan because plaintiffs failed to prove that the 4.22% total deviation in the Board’s plan is of a sufficient “size and quality to amount to an invidious discrimination under the Fourteenth Amendment.” Gaffney v. Cummings, 412 U.S. 735, 741, 93 S.Ct. 2321, 2325, 37 L.Ed.2d 298 (1973). Rather, defendants argue, the deviation is de minimis, and, therefore, the Board’s plan is constitutionally acceptable. Defendants argue in the alternative that, even if the total deviation is not de minimis, the Board’s plan is still acceptable because the state’s policy of maintaining the Board’s membership at fifteen is a sufficient justification for the 4.22% deviation.
The Supreme Court has declined to prescribe “any precise constitutional tests” for reviewing courts to use in determining whether a particular apportionment plan passes constitutional muster. Reynolds v. Sims, 377 U.S. 533, 578, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964). There is no fixed percentage deviation demarcating the de minimis from the unconstitutional, Kirkpatrick v. Preisler, 394 U.S. 526, 530-31, 89 S.Ct. 1225, 1228-29, 22 L.Ed.2d 519 (1969); each deviation must be examined on a case-by-case basis. “What is marginally permissible in one State may be unsatisfactory in another, depending on the particular circumstances of the case.” Reynolds v. Sims, 377 U.S. 533, 578, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964).
Initially, plaintiffs bear the burden of proving that the deviation from popula[487]*487tion equality is substantial. Gaffney v. Cummings, 412 U.S. 735, 745, 93 S.Ct. 2321, 2327, 37 L.Ed.2d 298 (1973). Once plaintiffs prove a prima facie case of discrimination, the burden shifts to defendants to show either that the deviation is unavoidable, Kirkpatrick v. Preisler, 394 U.S. 526, 531, 89 S.Ct. 1225, 1229, 22 L.Ed.2d 519 (1969), or that the deviation is justified by an attempt to effectuate a rational state policy. Reynolds v. Sims, 377 U.S. 533, 579, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964).
Although the Supreme Court has approved apportionment plans with a total deviation greater than 4.22%, 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); Abate v. Mundt, 403 U.S. 182, 91 S.Ct. 1904, 29 L.Ed.2d 399 (1971), in only two of the eases, White v. Regester, 412 U.S. 755, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973), and Gaffney v. Cummings, 412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973), did the Court find that the deviation was de minimis. In White, the Court held that a total deviation of 9.9% in the state house of representatives was de minimis, and in Gaffney, the Court held that a maximum deviation of 1.81% in the state senate and a 7.83% deviation in the state house of representatives were de minimis. In both cases the Court was examining a population deviation created by a multiple district apportionment plan. In this case, however, we are confronted with an apportionment plan that involves only two districts.
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BAUER, Circuit Judge.
Defendants appeal from the district court order requiring them to increase the size of the Board of Commissioners of Cook County (“Board”) from fifteen members, nine elected from Chicago and six from the suburbs, to seventeen members, ten elected from Chicago and seven from the suburbs. Defendants contend that the district court erred in ordering reapportionment because the plaintiffs failed to prove that the Board’s fifteen member apportionment plan diluted their voting rights in violation of the fourteenth amendment. We affirm.
I
Plaintiffs originally filed this reapportionment suit in 1973. They alleged that the Board, which then had fifteen members, ten elected from Chicago and five elected from the suburbs, overrepresented Chicago citizens by 4.87% and underrepresented suburban citizens by 4.87%. The district court held that the 9.74% total deviation diluted the voting rights of the suburban voters in violation of the fourteenth amendment. The court ordered the Board to increase its size to sixteen members, ten to be elected from the city and six from the suburbs. The court’s reapportionment plan decreased the total deviation to 1.4%, the smallest feasible deviation. Sutton v. Dunne, 365 F.Supp. 483 (N.D.Ill.1973). Defendants did not appeal the district court’s 1973 reapportionment order.
On October 15, 1973, the Board adopted an ordinance implementing the district court’s reapportionment plan. The 1974 and 1978 Board elections were held on the basis of that ordinance. On November 2, 1981, the Board passed an ordinance decreasing its size to fifteen members, nine to [486]*486be elected from the city and six from the suburbs. The Board’s 1981 apportionment plan was based on Cook County population figures from the 1980 census.
Plaintiffs returned to the district court to obtain modification of the court’s 1973 order to reflect 1980 population changes. Plaintiffs requested the court to reject the Board’s 1981 plan and order it to increase either to sixteen members, nine to be elected from the city and seven from the suburbs, or to seventeen members, ten to be elected from the city and seven from the suburbs. Using adjusted raw population figures from the 1980 census,1 the district court calculated that the Board’s 1981 plan created a 2.11% overrepresentation of Chicago citizens and a concomitant 2.11% un-derrepresentation of suburban citizens. The court held that the plan’s 4.22% total deviation violated the fourteenth amendment. The court also rejected the plaintiffs’ plan calling for a proposed sixteen member Board because that plan created an unacceptable 3.28% total deviation, with Chicago underrepresented by 1.64% and the suburbs overrepresented by a like amount. The court adopted the plaintiffs’ alternate plan and ordered the Board to increase its size to seventeen members, ten to be elected from Chicago and seven from the suburbs. The court found that this apportionment plan would result in a .93% underrepresen-tation of the suburbs and .93% overrepre-sentation of the city voters, with a total deviation of 1.86%. Sutton v. Dunne, 529 F.Supp. 312 (N.D.I11.1981).
II
Defendants claim that the district court erred in ordering them to adopt plaintiffs’ apportionment plan because plaintiffs failed to prove that the 4.22% total deviation in the Board’s plan is of a sufficient “size and quality to amount to an invidious discrimination under the Fourteenth Amendment.” Gaffney v. Cummings, 412 U.S. 735, 741, 93 S.Ct. 2321, 2325, 37 L.Ed.2d 298 (1973). Rather, defendants argue, the deviation is de minimis, and, therefore, the Board’s plan is constitutionally acceptable. Defendants argue in the alternative that, even if the total deviation is not de minimis, the Board’s plan is still acceptable because the state’s policy of maintaining the Board’s membership at fifteen is a sufficient justification for the 4.22% deviation.
The Supreme Court has declined to prescribe “any precise constitutional tests” for reviewing courts to use in determining whether a particular apportionment plan passes constitutional muster. Reynolds v. Sims, 377 U.S. 533, 578, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964). There is no fixed percentage deviation demarcating the de minimis from the unconstitutional, Kirkpatrick v. Preisler, 394 U.S. 526, 530-31, 89 S.Ct. 1225, 1228-29, 22 L.Ed.2d 519 (1969); each deviation must be examined on a case-by-case basis. “What is marginally permissible in one State may be unsatisfactory in another, depending on the particular circumstances of the case.” Reynolds v. Sims, 377 U.S. 533, 578, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964).
Initially, plaintiffs bear the burden of proving that the deviation from popula[487]*487tion equality is substantial. Gaffney v. Cummings, 412 U.S. 735, 745, 93 S.Ct. 2321, 2327, 37 L.Ed.2d 298 (1973). Once plaintiffs prove a prima facie case of discrimination, the burden shifts to defendants to show either that the deviation is unavoidable, Kirkpatrick v. Preisler, 394 U.S. 526, 531, 89 S.Ct. 1225, 1229, 22 L.Ed.2d 519 (1969), or that the deviation is justified by an attempt to effectuate a rational state policy. Reynolds v. Sims, 377 U.S. 533, 579, 84 S.Ct. 1362, 1390, 12 L.Ed.2d 506 (1964).
Although the Supreme Court has approved apportionment plans with a total deviation greater than 4.22%, 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); Abate v. Mundt, 403 U.S. 182, 91 S.Ct. 1904, 29 L.Ed.2d 399 (1971), in only two of the eases, White v. Regester, 412 U.S. 755, 93 S.Ct. 2332, 37 L.Ed.2d 314 (1973), and Gaffney v. Cummings, 412 U.S. 735, 93 S.Ct. 2321, 37 L.Ed.2d 298 (1973), did the Court find that the deviation was de minimis. In White, the Court held that a total deviation of 9.9% in the state house of representatives was de minimis, and in Gaffney, the Court held that a maximum deviation of 1.81% in the state senate and a 7.83% deviation in the state house of representatives were de minimis. In both cases the Court was examining a population deviation created by a multiple district apportionment plan. In this case, however, we are confronted with an apportionment plan that involves only two districts. Greater “mathematical exactness” between the number of citizens in each district and the number of their representatives is easier to attain when only two voter districts are involved than when multiple districts are involved. Therefore, the 4.22% total deviation in the Board’s 1981 plan, although perhaps an insubstantial deviation in a multi-district case, is not de minimis in this two district case.2
Defendants contend that the Board’s plan is constitutionally acceptable even though the 4.22% deviation is substantial because the Board’s policy of maintaining its membership at fifteen is a sufficient justification for the deviation. In Mahan v. Howell, 410 U.S. 315, 93 S.Ct. 979, 35 L.Ed.2d 320 (1973), and Abate v. Mundt, 403 U.S. 182, 91 S.Ct. 1904, 29 L.Ed.2d 399 (1971), the Supreme Court approved total deviations of 16.4% and 11.9%, respectively, on the ground that the deviations were justified by the state policy of preserving the integrity of political subdivisions and jurisdictional lines. Defendants argue that their dual policies of preserving the historical size of the Board and saving taxpayers the $80,400 per year that each additional member would cost likewise are rational justifications for a substantial deviation from population equality.
[488]*488Defendants’ reliance on Mahan and Abate, however, is misplaced. In those cases the Court recognized that the state may have a substantial interest in maintaining slightly unequal voting districts in order to provide representation to subdivisions qua subdivisions. Mahan v. Howell, 410 U.S. at 326, 93 S.Ct. at 986; Abate v. Mundt, 403 U.S. at 186, 91 S.Ct. at 1907. The Cook County Board, however, can achieve this goal without deviating from population equality simply by altering its size. The defendants’ arguments against making such an alteration are not persuasive. The Board has a total budget of almost $1,000,000,000. While the Board’s desire to save taxpayers’ $160,800 is laudable, it is not a sufficient justification for maintaining a 4.22% deviation from population equality. Nor is the Board’s desire to remain at fifteen members a sufficient justification — especially since the Illinois Constitution recognizes that it may be necessary to increase the Board’s size to insure population equality. Section 5(b) of the 1970 Illinois Constitution Transition Schedule provides that “the number of members of the Cook County Board shall be fifteen except that the county board may increase the number if necessary to comply with apportionment requirements.” The district court did not err in finding that the Board’s 1981 apportionment plan unconstitutionally diluted Cook County suburban citizens’ voting rights.
The district court ordered the Board to increase from fifteen to seventeen members and thereby decrease the total deviation from 4.22% to 1.86%. “We [will] not disapprove a court-imposed minor variation from a State’s prescribed figure when that change is shown to be necessary to meet constitutional requirements.” Sixty-Seventh Minnesota State Senate v. Beens, 406 U.S. 187, 199, 92 S.Ct. 1477, 1485, 32 L.Ed.2d 1 (1972) (per curiam). The judgment of the district court is
AFFIRMED.