The observed heritable variation in complex phenotypes can only partially be explained by mutation-selection balance. Directional selection is expected to remove most additive variation, so possible hypotheses for its maintenance include balancing selection, inefficient selection, or failure of populations to reach equilibrium . Looking at patterns of polymorphisms to corroborate these hypotheses mostly negative values of Tajima’s D have been observed in Drosophila (indicating selective sweeps or rapid population expansion). Here, we have established a panel of 170 nearly homozygous D. simulans genotypes from a single stable population and found that D is strongly biased towards positive values in the regions of normal recombination. We rule out demography, admixture, and balancing selection based on the patterns of linkage disequilibrium and Tajima’s D. Using recently developed statistical tests based on a measure of haplotype homozygosity (H12) we were able to detect numerous soft and hard sweeps and distinguish between them (H2/H1). We found evidence for abundant incomplete soft sweeps, including that they are much more numerous than in comparable populations of D. melanogaster. We hypothesize that transient selective sweeps might be responsible for the bulk of phenotypic variation in complex traits. This is a potential explanation for the excess of variation observed in most traits compared to theoretical expectations.