Progression through mitosis is controlled by protein degradation that is mediated by the anaphase-promoting complex/cyclosome (APC/C) and its associated specificity factors. In budding yeast, APC/CCdc20 promotes the degradation of the Pds1p anaphase inhibitor at the metaphase-to-anaphase transition, whereas APC/CCdh1 promotes the degradation of the mitotic cyclins at the exit from mitosis. Here we show that Pds1p has a novel activity as an inhibitor of mitotic cyclin destruction, apparently by preventing the activation of APC/CCdh1. This activity of Pds1p is independent of its activity as an anaphase inhibitor. We propose that the dual role of Pds1p as an inhibitor of anaphase and of cyclin degradation allows the cell to couple the exit from mitosis to the prior completion of anaphase. Finally, these observations provide a novel regulatory paradigm in which the sequential degradation of two substrates is determined by the substrates themselves, such that an early substrate inhibits the degradation of a later one.