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.