Repair of DNA double-stranded breaks (DSBs) is crucial for the maintenance of genome stability. DSBs are repaired by either error prone non-homologous end-joining (NHEJ) or error-free homologous recombination. NHEJ precedes either by a classic, Lig4-dependent process (C-NHEJ) or an alternative, Lig4-independent one (A-NHEJ). Dysfunctional telomeres arising either through natural attrition due to telomerase deficiency or by removal of telomere-binding proteins are recognized as DSBs. In this report, we studied which end-joining pathways are required to join dysfunctional telomeres. In agreement with earlier studies, depletion of Trf2 resulted in end-to-end chromosome fusions mediated by the C-NHEJ pathway. In contrast, removal of Tpp1-Pot1a/b initiated robust chromosome fusions that are mediated by A-NHEJ. C-NHEJ is also dispensable for the fusion of naturally shortened telomeres. Our results reveal that telomeres engage distinct DNA repair pathways depending on how they are rendered dysfunctional, and that A-NHEJ is a major pathway to process dysfunctional telomeres.