We investigate how different rates of environmental change affect adaptive outcomes and dynamics by selecting Chlamydomonas populations for over 200 generations in environments where the rate of change varies. We find that slower rates of environmental change result in end populations that grow faster and pay a lower cost of adaptation than populations that adapt to a sudden change of the same magnitude. We detected partial selective sweeps in adapting populations by monitoring changes in marker frequency in each population. Although populations adapting to a sudden environmental change showed evidence of mutations of large effect segregating early on, populations adapting to slow rates of change showed patterns that were consistent with mutations of relatively small effect occurring at less predictable times. This work suggests that rates of environmental change may fundamentally alter adaptive dynamics and outcomes of adaptation by changing the size and timing of fitness increases. We suggest that using mutations of smaller effect during adaptation may result in lower levels of pleiotropy and historical constraints, which could in turn result in higher fitness by the end of the experiment.