We use near-source (10 to 164 km) displacement seismograms to image the slip distribution and rupture history of the 28 June 1992 Mw = 7.3 Landers, California, earthquake. Aftershock seismograms from similar distances are modeled to find the velocity model and frequency range (0.05 to 0.25 Hz) over which theoretical Green's functions are most accurate, and the measure of fit is used as an upper bound on theoretical error in the mainshock inversion. We represent the rupture surface with three planar segments divided into 3 by 3 km elements extending from the surface to 18-km depth, and solve for the slip distribution and the rupture time model that minimizes misfit to both recorded seismograms, and mapped surface displacement in a least-squares sense. We investigate two faulting models, one with a uniformly short (<3 sec) rise time everywhere on the fault surface and the other with a variable rise time (2 to 6 sec). We perform sensitivity tests using synthetic data from a hypothetical earthquake to evaluate model resolution and solution stability. In the sensitivity tests, both fault models recover similar slip and rupture features, but neither is capable of imaging details of the rise time. For the Landers earthquake, we find an average rupture velocity of 2.5 km/sec and use this average for a starting model in a linearized inversion for rupture time. In our solutions of slip-amplitude distribution, the southernmost, Johnson Valley fault segment has 20% of the total seismic moment (6 to 8 × 1019 N-m) with small displacements near the hypocenter; the Homestead Valley segment contributes half of the moment with the largest slip amplitudes 25 to 35 km northwest of the hypocenter at 4 to 12-km depth; and the Camp Rock-Emerson segment contributes the remaining moment with the largest slip amplitude 35 to 50 km northwest of the hypocenter in the shallow crust (<9 km). There is some evidence that the rupture front is delayed as it encounters high-slip regions, suggesting that prior to the mainshock these areas were further from failure owing either to greater strength or lower prestress.