Telomeres hide (or 'cap') chromosome ends from DNA-damage surveillance mechanisms that arrest the cell cycle and promote repair, but the checkpoint status of telomeres is not well understood. Here we characterize the response in Saccharomyces cerevisiae to DNA double-strand breaks (DSBs) flanked by varying amounts of telomeric repeat sequences (TG(1-3)). We show that even short arrays of TG(1-3) repeats do not induce G2/M arrest. Both Rif1 and Rif2 are required for capping at short, rapidly elongating ends, yet are largely dispensable for protection of longer telomeric arrays. Rif1 and Rif2 act through parallel pathways to block accumulation of both RPA and Rad24, activators of checkpoint kinase Mec1 (ATR). Finally, we show that Rif function is correlated with an 'anticheckpoint' effect, in which checkpoint recovery at an adjacent unprotected end is stimulated, and we provide insight into the molecular mechanism of this phenomenon.