An unusual feature of bacteria in the genus Borrelia (causative agents of Lyme disease and relapsing fever) is a segmented genome consisting of multiple linear DNA molecules with covalently closed hairpin ends, known as telomeres. The hairpin telomeres are generated by a DNA breakage and reunion process (telomere resolution) promoted by ResT, an enzyme using an active site related to that of tyrosine recombinases and type IB topoisomerases. In this study, we define the minimal sequence requirements for a functional telomere and identify specific basepairs that appear to be important for telomere resolution. In addition, we show that the two naturally occurring and distinct telomere spacings found in B. burgdorferi can both be efficiently processed by ResT. This flexibility for substrate utilization by ResT supports the argument for a single telomere resolvase in Borrelia. Furthermore, although telomere recognition requires sequence specificity in part of the substrate, DNA cleavage is instead position dependent and occurs at a fixed distance from the axis of symmetry and the conserved sequence of box 3 in the different replicated telomere substrates. This positional dependence for DNA cleavage has not been observed previously for a tyrosine recombinase.