The anaphase-promoting complex or cyclosome (APC/C) initiates mitotic exit by ubiquitylating cell-cycle regulators such as cyclin B1 and securin. Lys 48-linked ubiquitin chains represent the canonical signal targeting proteins for degradation by the proteasome, but they are not required for the degradation of cyclin B1. Lys 11-linked ubiquitin chains have been implicated in degradation of APC/C substrates, but the Lys 11-chain-forming E2 UBE2S is not essential for mitotic exit, raising questions about the nature of the ubiquitin signal that targets APC/C substrates for degradation. Here we demonstrate that multiple monoubiquitylation of cyclin B1, catalysed by UBCH10 or UBC4/5, is sufficient to target cyclin B1 for destruction by the proteasome. When the number of ubiquitylatable lysines in cyclin B1 is restricted, Lys 11-linked ubiquitin polymers elaborated by UBE2S become increasingly important. We therefore explain how a substrate that contains multiple ubiquitin acceptor sites confers flexibility in the requirement for particular E2 enzymes in modulating the rate of ubiquitin-dependent proteolysis.