SignificanceProteins that bind nucleic acids are frequently categorized as being either specific or nonspecific, with interfaces to match that activity. In this study, we have found that a telomere-binding protein exhibits a degree of specificity for ssDNA that is finely tuned for its function, which includes specificity for G-rich sequences with some tolerance for substitution. Mutations of the protein that dramatically impact its affinity for single-stranded telomeric DNA are lethal, as expected; however, mutations that alter specificity also impact biological function. Unexpectedly, we found mutations that make the protein more specific are also deleterious, suggesting that specificity and nonspecificity in nucleic acid recognition may be achieved through more nuanced mechanisms than currently recognized.