Ubiquitin-dependent proteolysis mediated by the anaphase-promoting complex/cyclosome (APC/C) ubiquitin ligase lies at the heart of the cell cycle. The APC/C targets mitotic cyclins for destruction in mitosis and G1 phase and is then inactivated at S phase, thereby generating the alternating states of high and low cyclin-Cdk activity required for the alternation of mitosis and DNA replication. Two key questions are how the APC/C is held in check by the spindle-assembly checkpoint to delay cells in mitosis in the presence of improperly attached chromosomes, and how the APC/C is inactivated once cells exit mitosis. The ubiquitin-conjugating protein UbcH10 has been proposed to be crucial in the answers to both questions. However, here we show that the behaviour of UbcH10 is inconsistent with both a crucial role in the spindle checkpoint and in inactivating the APC/C as part of an autonomous oscillator. Instead, we find that the rate-limiting role of UbcH10 is only at the end of G1 phase, just before DNA replication begins.