Broadband teleseismic P waves have been analyzed to recover the rupture history of the large (M(s) 7.4) Colima-Jalisco, Mexico, shallow interplate thrust earthquake of 9 October 1995. Ground-displacement records in the period range of 1-60 sec are inverted using a linear, finite-fault waveform inversion procedure that allows a variable dislocation duration on a prescribed fault. The method is applied using both a narrow fault that simulates a line source with a dislocation window of 50 sec and a wide fault with a possible rise time of up to 20 sec that additionally allows slip updip and downdip from the hypocenter. The line-source analysis provides a spatio-temporal image of the slip distribution consisting of several large sources located northwest of the hypocenter and spanning a range of rupture velocities. The two-dimensional finite-fault inversion allows slip over this rupture-velocity range and indicates that the greatest coseismic displacement (3-4 m) is located between 70 and 130 km from the hypocenter at depths shallower than about 15 km. Slip in this shallow region consists of two major sources, one of which is delayed by about 10 sec relative to a coherent propagation of rupture along the plate interface. These two slip sources account for about one-third of the total P-wave seismic moment of 8.3 X 1027 dyne-cm (M(w) 7.9) and may have been responsible for the local tsunami observed along the coast following the earthquake.