An important design issue in allelic association studies for mapping disease genes is the choice of markers. We have used a simple model of a founder population, similar to those of Ott & Rabinowitz (1997) and Chapman & Wijsman (1998), to explore the effect of the number of alleles at a marker polymorphism on the power to detect linkage disequilibrium due to single or multiple ancestral disease mutations. We show that the optimal number of alleles is more than 2 even in the case of a single ancestral disease mutation, and much higher still if multiple ancestral mutations are present. In large samples, much power is lost by using too few alleles, but relatively little power is lost by using too many alleles. These results confirm the desirability of using highly polymorphic markers or multi-locus haplotypes for association analysis. They also show that multiple ancestral disease mutations do not necessarily preclude linkage disequilibrium mapping, if highly polymorphic markers or multi-locus haplotypes are used.