Adaptation in eukaryotes is generally assumed to be mutation-limited because of small effective population sizes. This view is difficult to reconcile, however, with the observation that adaptation to anthropogenic changes, such as the introduction of pesticides, can occur very rapidly. Here we investigate adaptation at a key insecticide resistance locus (Ace) in Drosophila melanogaster and show that multiple simple and complex resistance alleles evolved quickly and repeatedly within individual populations. Our results imply that the current effective population size of modern D. melanogaster populations is likely to be substantially larger (> or = 100-fold) than commonly believed. This discrepancy arises because estimates of the effective population size are generally derived from levels of standing variation and thus reveal long-term population dynamics dominated by sharp--even if infrequent--bottlenecks. The short-term effective population sizes relevant for strong adaptation, on the other hand, might be much closer to census population sizes. Adaptation in Drosophila may therefore not be limited by waiting for mutations at single sites, and complex adaptive alleles can be generated quickly without fixation of intermediate states. Adaptive events should also commonly involve the simultaneous rise in frequency of independently generated adaptive mutations. These so-called soft sweeps have very distinct effects on the linked neutral polymorphisms compared to the standard hard sweeps in mutation-limited scenarios. Methods for the mapping of adaptive mutations or association mapping of evolutionarily relevant mutations may thus need to be reconsidered.