The completion of mitosis depends on protein ubiquitination by the anaphase-promoting complex (APC). The APC is activated by association with Cdc20 in midmitosis and Cdh1 in late mitosis and G1. Here, we show that in budding yeast the activation of APC(Cdh1) is controlled in part by destruction of the Cdh1 inhibitor Acm1. We find that Acm1 uses pseudosubstrate and other sequence motifs to bind and inhibit Cdh1, but not Cdc20. Acm1 also contains a destruction sequence that promotes its ubiquitination by APC(Cdc20), resulting in the disappearance of Acm1 in early anaphase. Later in mitosis, Acm1 destruction is also promoted by APC(Cdh1). Finally, Cdk1-dependent phosphorylation of Acm1 modulates its localization and destruction. We conclude that ubiquitination of a Cdh1 inhibitor by APC(Cdc20) helps establish the order of activation of the two APC isoforms. We also speculate that the ability of APC(Cdh1) to target its own inhibitor enhances the bistability of the late mitotic regulatory system.