Most evolving populations are subdivided into multiple subpopulations connected to each other by varying levels of gene flow. However, how population structure and gene flow (i.e., migration) affect adaptive evolution is not well understood. Here, we studied the impact of migration on asexually reproducing evolving computer programs (digital organisms). We found that digital organisms evolve the highest fitness values at intermediate migration rates, and we tested three hypotheses that could potentially explain this observation: (i) migration promotes passage through fitness valleys, (ii) migration increases genetic variation, and (iii) migration reduces clonal interference through a process called "leapfrogging". We found that migration had no appreciable effect on the number of fitness valleys crossed and that genetic variation declined monotonously with increasing migration rates, instead of peaking at the optimal migration rate.However, the number of leapfrogging events, in which a superior beneficial mutation emerges on a genetic background that predates the previously best genotype in the population, did peak at the optimal migration rate. We thus conclude that in structured, asexual populations intermediate migration rates allow for optimal exploration of multiple, distinct fitness peaks, and thus yield the highest long-term adaptive success.