Mutations not only alter allele frequencies in a genetic pool but may also determine the fate of an evolutionary process. Here we study which allele fixes in a one-step, one-way model including the wild type and two adaptive mutations. We study the effect of the four basic evolutionary mechanisms-genetic drift, natural selection, mutation, and gene flow-on mutant fixation and its kinetics. Determining which allele is more likely to fix is not simply a question of comparing fitnesses and mutation rates. For instance, if the allele of interest is less fit than the other, then not only must it have a greater mutation rate, but also its mutation rate must exceed a specific threshold for it to prevail. We find exact expressions for such conditions. Our conclusions are based on the mathematical description of two extreme but important regimes, as well as on simulations.