Abstract Considerable interest is focused on the use of polymorphism data to identify regions of the genome that underlie recent adaptations. These searches are guided by a simple model of positive selection, in which a mutation is favored as soon as it arises. This assumption may not be realistic, as environmental changes and range expansions may lead previously neutral or deleterious alleles to become beneficial. We examine what effect this mode of selection has on patterns of variation at linked neutral sites by implementing a new coalescent model of positive directional selection on standing variation. In this model, a neutral allele arises and drifts in the population, then at frequency f becomes beneficial, and eventually reaches fixation. Depending on the value of f, this scenario can lead to a large variance in allele frequency spectra and in levels of linkage disequilibrium at linked, neutral sites. In particular, for intermediate f, the beneficial substitution often leads to a loss of rare alleles–a pattern that differs markedly from the signature of directional selection currently relied on by researchers. These findings highlight the importance of an accurate characterization of the effects of positive selection, if we are to reliably identify recent adaptations from polymorphism data.