A new method is presented to invert for the moment tensor and depth using the amplitude spectra of vertical-component Rayleigh waves in the period range 20 to 100 sec. The technique follows a similar approach to that suggested by Romanowicz (1982a) to invert for the moment tensor from the complex spectra of Rayleigh waves and presents some distinct advantages to the method proposed originally by Mendiguren (1977). It eliminates some biases and errors in the data arising, for example, from inaccurate propagation corrections. Furthermore, it is substantially faster computationally and permits us to study independently the variance reduction as a function of depth of each of the momenttensor elements, resulting in better focal depth resolution. The method is applied to three earthquakes in the Tien Shan Mountains of Central Asia, the Eastern Cordillera of Peru, and the Gibbs Transform fault in the North Atlantic. In all three cases, the results of the moment-tensor inversion agree with those determined using long-period body-wave modeling.