Phase times for an ensemble of 20 aftershocks of the June 1, 1975, Galway Lake earthquake were inverted to determine hypocenters and local velocity structure simultaneously. A maximum likelihood formulation of linear, least-squares inversion was used so that the data were weighted according to their estimated variances. A trade-off parameter controlled the relative importance of the RMS error and the amount by which the model changed at each iteration. Individual aftershocks must be selected so that a wide variety of travel paths are represented. Initial trials disclosed that careful constraints are necessary for allowed changes in station delays. Fixed velocity boundaries, based on a priori information, were used for each of several starting models, and only layer velocities were allowed to vary. Each of the trials indicated that shallow crustal velocities in the vincinity of Galway Lake are somewhat lower than those of the usual velocity models. The velocities are not strongly constrained by this data set, but the results are consistent with a subsequent, detailed refraction survey by other workers. Mapping the travel-time surface in time-depth-distance space helps clarify the limitations inherent in a given problem.