Tumor suppressor p53-binding protein 1 (53BP1) regulates the repair of dysfunctional telomeres lacking the shelterin protein TRF2 by promoting their mobility, their nonhomologous end-joining (NHEJ), and, as we show here, by blocking 5′ resection by CtIP. We report that these functions of 53BP1 required its N-terminal ATM/ATR target sites and its association with H4K20diMe, but not the BRCT domain, the GAR domain, or the binding of 53BP1 to dynein. A mutant lacking the oligomerization domain (53BP1 ^oligo ) was only modestly impaired in promoting NHEJ of dysfunctional telomeres and showed no defect with regard to the repression of CtIP. This 53BP1 ^oligo allele was previously found to be unable to support class switch recombination or to promote radial chromosome formation in PARP1 inhibitor-treated Brca1-deficient cells. The data therefore support two conclusions. First, the requirements for 53BP1 in mediating NHEJ at dysfunctional telomeres and in class switch recombination are not identical. Second, 53BP1-dependent repression of CtIP at double-strand breaks (DSBs) is unlikely to be sufficient for the generation of radial chromosomes in PARP1 inhibitor-treated Brca1-deficient cells.