TLS is an optimized transit-fitting algorithm to search for periodic transits of small planets. In contrast to BLS: Box Least Squares (ascl:1607.008), which searches for rectangular signals in stellar light curves, TLS searches for transit-like features with stellar limb-darkening and including the effects of planetary ingress and egress. TLS also analyses the entire, unbinned data of the phase-folded light curve. TLS yields a ~10% higher detection efficiency (and similar false alarm rates) compared to BLS though has a higher computational load. This load is partly compensated for by applying an optimized period sampling and transit duration sampling constrained to the physically plausible range.