The design and interpretation of genetic association studies depends on the relationship between the genotyped variants and the underlying functional variant, often parameterized as the squared correlation or r2 measure of linkage disequilibrium between two loci. While it has long been recognized that placing a constraint on the r2 between two loci also places a constraint on the difference in frequencies between the coupled alleles, this constraint has not been quantified. Here, quantification of this severe constraint is presented. For example, for r2 ≥ .8, the maximum difference in allele frequency is ± .06 which occurs when one locus has allele frequency .5. For r2 ≥ .8 and allele frequency at one locus of .1, the maximum difference in allele frequency at the second locus is only ± .02. The impact on the design and interpretation of association studies is discussed.