In the classical model of molecular adaptation, a favored allele derives from a single mutational origin. This ignores that beneficial alleles can enter a population recurrently, either by mutation or migration, during the selective phase. In this case, descendants of several of these independent origins may contribute to the fixation. As a consequence, all ancestral haplotypes that are linked to any of these copies will be retained in the population, affecting the pattern of a selective sweep on linked neutral variation. In this study, we use analytical calculations based on coalescent theory and computer simulations to analyze molecular adaptation from recurrent mutation or migration. Under the assumption of complete linkage, we derive a robust analytical approximation for the number of ancestral haplotypes and their distribution in a sample from the population. We find that so-called "soft sweeps," where multiple ancestral haplotypes appear in a sample, are likely for biologically realistic values of mutation or migration rates.