Background: Divergence of two independently evolving sequences that originated from a common ancestor can be described by two parameters, the asymptotic level of divergence E and the rate r at which this level of divergence is approached. Constant negative selection impedes allele replacements and, therefore, is routinely assumed to decelerate sequence divergence. However, its impact on E and on r has not been formally investigated.Results: Strong selection that favors only one allele can make E arbitrarily small and r arbitrarily large. In contrast, in the case of 4 possible alleles and equal mutation rates, the lowest value of r, attained when two alleles confer equal fitnesses and the other two are strongly deleterious, is only two times lower than its value under selective neutrality.Conclusions: Constant selection can strongly constrain the level of sequence divergence, but cannot reduce substantially the rate at which this level is approached. In particular, under any constant selection the divergence of sequences that accumulated one substitution per neutral site since their origin from the common ancestor must already constitute at least one half of the asymptotic divergence at sites under such selection.Reviewers: This article was reviewed by Drs. Nicolas Galtier, Sergei Maslov, and Nick Grishin.