Timely ubiquitin-mediated protein degradation is fundamental to cell cycle control, but the precise degradation order at each cell cycle phase transition is still unclear. In this work, we investigated the degradation order of targets of a single human E3 ubiquitin ligase important for S-phase proteolysis, known as CRL4Cdt2. We showed that in both synchronized cells and asynchronously proliferating cells, CRL4Cdt2-mediated degradation of the cell cycle proteins Cdt1, p21, and PR-Set7 occurs in a consistent order during both the G1/S transition and during DNA repair synthesis. We additionally showed that these different rates of degradation are determined by the CRL4Cdt2 targeting motif called a PCNA interacting peptide (PIP) degron, which allows for substrate binding to DNA-bound proliferating cell nuclear antigen (PCNA) and recognition by CRL4Cdt2. Manipulating the degradation order such that p21 was degraded prematurely promoted stalled replication in mid-S phase and sensitivity to replication arrest. Collectively, these results establish for the first time that ordered degradation at the G1/S transition, facilitated by the CRL4Cdt2 E3 ligase, is important to avoid replication stress and genome instability. Another process that is tightly controlled at cell cycle transitions is replication origin licensing, in which replication initiation sites, or origins, are rendered competent for replication by the DNA loading of the replicative helicase, the Mini-Chromosome Maintenance (MCM) complex. Through the collective action of ORC, Cdc6, and Cdt1 proteins, MCM complexes are loaded onto DNA exclusively in G1 phase in an inactive form, and become activated by protein kinases during S phase. MCM loading is strictly inhibited beyond the G1/S transition and during cellular quiescence (G0 phase), although at the time of this study, mechanisms contributing to this licensing block specifically during G0 phase were poorly understood. To identify novel protein mediators of quiescence establishment and maintenance, we performed a mass spectrometry screen designed to identify differential MCM binding partners in quiescent vs. proliferating cells. We prioritized several novel MCM interactions uncovered from this initial screen for further validation experiments, including three with previously characterized roles in the control of cell proliferation/quiescence: Sam68 (KHDRBS1), Nme1, and Host Cell Factor C1 (HCFC1). Future work will be needed to improve the initial screening approach and to establish a role for these new MCM interactions in cell cycle control and/or MCM loading regulation.