We compare three relative earthquake location techniques using tests on synthetic data that simulate many of the statistical properties of real travel time data. The methods are (1) the hypocentroidal decomposition method of Jordan and Sverdrup (1981), (2) the source-specific station term method (SSST) of Richards-Dinger and Shearer (2000), and (3) the modified double-difference method (DD) of Waldhauser and Ellsworth (2000). We generate a set of synthetic earthquakes, stations, and arrival time picks in half-space velocity models. We simulate the effect of travel time variations caused by random picking errors, station terms, and general three-dimensional velocity structure. We implement the algorithms with a common linearized approach and solve the systems using a conjugate gradient method. We constrain the mean location shift to be zero for the hypocentroidal decomposition and double-difference locations. For a single compact cluster of events, these three methods yield very similar improvements in relative location accuracy. For distributed seismicity, the DD and SSST algorithms both provide improved relative locations of comparable accuracy. We also present a new location technique, termed the shrinking box SSST method, which provides some improvement in absolute location accuracy compared to the SSST method. In our implementation of these algorithms, the SSST method runs significantly faster than the DD method.