A single double-stranded DNA (dsDNA) break will cause yeast cells to arrest in G2/M at the DNA damage checkpoint. If the dsDNA break cannot be repaired, cells will eventually override (that is, adapt to) this checkpoint, even though the damage that elicited the arrest is still present. Here, we report the identification of two adaptation-defective mutants that remain permanently arrested as large-budded cells when faced with an irreparable dsDNA break in a nonessential chromosome. This adaptation-defective phenotype was entirely relieved by deletion of RAD9, a gene required for the G2/M DNA damage checkpoint arrest. We show that one mutation resides in CDC5, which encodes a polo-like kinase, whereas a second, less penetrant, adaptation-defective mutant is affected at the CKB2 locus, which encodes a nonessential specificity subunit of casein kinase II.