We examine the ability of teleseismic P waves to identify the rupture history of large earthquakes along the Mexico subduction zone using a kinematic finite-fault waveform inversion scheme that uses the earthquake seismic moment to stabilize the inversion process. Application of our procedure to the teleseismic displacement waveforms recorded for the Mw 7.9 Colima–Jalisco earthquake of October 1995 yields a slip pattern that is similar to the rupture model derived previously using a more traditional approach that incorporates stepwise adjustments to the constraint equations to recover the least-complicated source model. The areas of large slip inferred for both models are located at the same general position along the fault, although peak slips obtained using the moment-constrained approach are significantly greater. Synthetic tests conducted for a hypothetical interplate rupture along the Guerrero portion of the Mexico subduction zone indicate that the high peak slips result from a wide variability in slip amplitude for individual subfaults, although the variability is less pronounced when velocity waveforms are used in the inversion. The tests also show that errors in fault dip and earthquake nucleation depth affect the accuracy of the inferred slip source more significantly than errors in strike and rake. Also, the data are relatively insensitive to variations in rupture velocity and dislocation duration, suggesting that our single-step approach could be used in a simplified manner to identify the first-order rupture features of large earthquakes using routinely derived fault parameters. A simplified analysis of the P-wave ground velocities recorded for the Mw 7.5 Tecomán, Colima, earthquake of January 2003 yields a slip distribution that is remarkably similar to a rupture model derived previously using teleseismic body waves and strong-motion records.