The design and interpretation of genome scans for selection have been largely influenced by models that assume either continuous directional selection on unconditionally beneficial new mutations (“hard” or “classic” sweeps) or fluctuating selection on a previously neutral or weakly-deleterious mutation (“soft” sweeps). However, many examples of adaptive phenotypes in natural population involve complex traits, and the above models may not be adequate descriptions of how such complex polygenic traits evolve. Here, I use forward-time simulation to examine the dynamics of adaptation to a sudden environmental shift, which is modeled as a shift in the optimum value of a complex trait with a broad-sense heritability less than one. The model integrates the existing concepts of “soft” sweeps from standing variation and “classic/hard” sweeps from new mutations, but the strength of selection on individual mutations changes over time as the mean trait value approaches the new optimum value. Adaptation initially proceeds via soft sweeps, fixing mutations of relatively large effect that arose prior to the optimum shift. Subsequent evolution involves hard sweeps of mutations whose effect sizes decrease as time goes on. The site frequency spectrum (SFS) and linkage disequilibrium (LD) show time-dependent deviations from equilibrium values, providing a means of inferring the magnitude of the optimum shift. Finally, the genetic variation for fitness takes a long time to return to equilibrium, and there is continued directional selection after the new optimum phenotype is reached as the population is loses mutations that increase variance in fitness.