A population genetical model is investigated in which the organism either alternates between diploid and haploid states or lives entirely in the haploid state. The behavior of the organism is determined by the genotype at a modifier locus. At an independent locus deleterious mutations occur at a low but constant frequency. It is found that the haploid behavior is always an evolutionarily attainable stable trait, while the ploidy-cyclic behavior is an evolutionarily attainable stable trait only when a certain condition holds. This condition depends on the strength of selection, the degree of ``sheltering'' given by the heterozygote state, and the degree of linkage between the modifier locus and the locus under selection. The last result leads to the speculation that the eukaryotes are derived from an organism which first developed more than one chromosome before it evolved the ploidy cycle.