Sex is thought to facilitate accumulation of initially rare beneficial mutations by allowing simultaneous allele replacements at many loci. However, this advantage of sex depends on a restrictive assumption that the fitness of a genotype is determined by fitness potential, a single intermediate variable to which all loci contribute additively, so that new alleles can accumulate in any order. Individual-based simulations of sexual and asexual populations reveal that under generic selection, sex often retards adaptive evolution. When new alleles are beneficial only if they accumulate in a prescribed order, a sexual population may evolve two or more times slower than an asexual population because only asexual reproduction allows some overlap of successive allele replacements. Many other fitness surfaces lead to an even greater disadvantage of sex. Thus, either sex exists in spite of its impact on the rate of adaptive allele replacements, or natural fitness surfaces have rather specific properties, at least at the scale of intrapopulation genetic variability.