Sirtuins comprise a family of enzymes that catalyze the deacetylation of acetyllysine side chains in a reaction that consumes NAD+. Although several crystal structures of sirtuins bound to non-native acetyl peptides have been determined, relatively little about how sirtuins discriminate among different substrates is understood. We have carried out a systematic structural and thermodynamic analysis of several peptides bound to a single sirtuin, the Sir2 homologue from Thermatoga maritima (Sir2Tm). We report structures of five different forms of Sir2Tm: two forms bound to the p53 C-terminal tail in the acetylated and unacetylated states, two forms bound to putative acetyl peptide substrates derived from the structured domains of histones H3 and H4, and one form bound to polypropylene glycol (PPG), which resembles the apoenzyme. The structures reveal previously unobserved complementary side chain interactions between Sir2Tm and the first residue N-terminal to the acetyllysine (position -1) and the second residue C-terminal to the acetyllysine (position +2). Isothermal titration calorimetry was used to compare binding constants between wild-type and mutant forms of Sir2Tm and between additional acetyl peptide substrates with substitutions at positions -1 and +2. The results are consistent with a model in which peptide positions -1 and +2 play a significant role in sirtuin substrate binding. This model provides a framework for identifying sirtuin substrates.