We study levels of X-linked vs. autosomal diversity using a model developed to analyze the hitchhiking effect. Repeated bouts of hitchhiking are thought to lower X-linked diversity for two reasons: first, because sojourn times of beneficial mutations are shorter on the X, and second, because adaptive substitutions may be more frequent on the X. We investigate whether each of these effects does, in fact, cause reduced X-linked diversity under hitchhiking. We study the strength of the hitchhiking effect on the X vs. autosomes when there is no recombination and under two different recombination schemes. When recombination occurs in both sexes, X-linked vs. autosomal diversity is reduced by hitchhiking under a broad range of conditions, but when there is no recombination in males, as in Drosophila, the required conditions are considerably more restrictive.