Directional environmental change is a ubiquitous phenomenon that may have profound effects on all living organisms. However, it is unclear how different rates of such change affect the dynamics and outcome of evolution. We studied this question using experimental evolution of heavy metal tolerance in the baker´s yeast Saccharomyces cerevisiae. To this end, we grew replicate lines of yeast for 500 generations in the presence of (i) a constant high concentration of cadmium, nickel or zinc, or (ii) a gradually increasing concentration of these metals. We found that gradual environmental change leads to a delay in fitness increase compared to abrupt change, but not necessarily to a different fitness of evolutionary endpoints. For the non-essential metal cadmium this delay is due to reduced fitness differences between genotypes at low metal concentrations, consistent with directional selection to minimize intracellular concentrations of this metal. In contrast, for the essential metals nickel and zinc different genotypes are selected at different concentrations, consistent with stabilizing selection to maintain constant intracellular concentrations of these metals. These findings indicate diverse fitness consequences of evolved tolerance mechanisms for essential and non-essential metals, and imply that the rate of environmental change and the nature of the stressor are crucial determinants of evolutionary dynamics.