Eukaryotic genome integrity is safeguarded by two highly conserved protein kinases that are called ATR and ATM for humans and Mec1 and Tel1 for Saccharomyces cerevisiae. Although they share sequence similarities and substrates, these protein kinases perform different specialized functions. In particular, Mec1 plays a key role in the DNA damage checkpoint response, whereas Tel1 primarily is involved in telomere homeostasis, and its checkpoint function is masked by the prevailing activity of Mec1. In order to understand how this specificity is achieved, we searched for TEL1 mutations able to compensate for the lack of Mec1 functions. Here, we describe seven independent dominant TEL1-hy alleles that are able to suppress, to different extents, both the hypersensitivity to genotoxic agents and the checkpoint defects of Mec1-deficient cells. Most of these alleles also cause telomere overelongation. In vitro kinase activity was increased compared to that of wild-type Tel1 in the Tel1-hy385, Tel1-hy394, Tel1-hy680, and Tel1-hy909 variants, but its activity was not affected by the TEL1-hy184 and TEL1-hy628 mutations and was slightly reduced by the TEL1-hy544 mutation. Thus, the phenotypes caused by at least some Tel1-hy variants are not simply the consequence of improved catalytic activity. Further characterization shows that Tel1-hy909 not only can sense and signal a single double-stranded DNA break, unlike wild-type Tel1, but also contributes more efficiently than Tel1 to single-stranded DNA accumulation at double-strand ends, thus enhancing Mec1 signaling activity. Moreover, it causes unscheduled checkpoint activation in unperturbed conditions and upregulates the checkpoint response to small amounts of DNA lesions. Finally, Tel1-hy544 can activate the checkpoint more efficiently than wild-type Tel1, while it causes telomere shortening, indicating that the checkpoint and telomeric functions of Tel1 can be separable.