DNA replication initiation in S. cerevisiae is promoted by B-type cyclin-dependent kinase (Cdk) activity. In addition, once-per-cell-cycle replication is enforced by cyclin-Cdk-dependent phosphorylation of the prereplicative complex (pre-RC) components Mcm2-7, Cdc6, and Orc1-6. Several of these controls must be simultaneously blocked by mutation to obtain rereplication. We looked for but did not obtain strong evidence for cyclin specificity in the use of different mechanisms to control rereplication: both the S-phase cyclin Clb5 and the mitotic cyclins Clb1-4 were inferred to be capable of imposing ORC-based and MCM-based controls. We found evidence that the S-phase cyclin Clb6 could promote initiation of replication without blocking reinitiation, and this activity was highly toxic when the ability of other cyclins to block reinitiation was prevented by mutation. The failure of Clb6 to regulate reinitiation was due to rapid Clb6 proteolysis, since this toxic activity of Clb6 was lost when Clb6 was stabilized by mutation. Clb6-dependent toxicity is also relieved when early accumulation of mitotic cyclins is allowed to impose rereplication controls. Cell-cycle timing of rereplication control is crucial: sufficient rereplication block activity must be available as soon as firing begins. DNA rereplication induces DNA damage, and when rereplication controls are compromised, the DNA damage checkpoint factors Mre11 and Rad17 provide additional mechanisms that maintain viability and also prevent further rereplication, and this probably contributes to genome stability.