A least squares joint inversion for regional and teleseismic waveforms is presented. The mean square error between seismograms and synthetics is minimized using true amplitudes. Matching true amplitudes in modeling requires meaningful estimates of modeling uncertainties and of seismogram signal-to-noise ratios. This also permits calculating linearized uncertainties on the solution based on accuracy and resolution. We use a priori estimates of earthquake parameters to stabilize unresolved parameters, and for comparison with a posteriori uncertainties. We verify the technique on synthetic data, and on the 1983 Borah Peak, Idaho (M=7.3), earthquake. We demonstrate the inversion on the August 1954 Rainbow Mountain, Nevada (M=6.8), earthquake and find parameters consistent with previous studies. ¿ American Geophysical Union 1988