Amplitude data from direct and near-source reflected phases are inverted to obtain point-source moment tensors. The inversion scheme is computationally efficient, and the results can be interpreted without the uniqueness problems that plague many geophysical inversion schemes. This follows from the linear relationship between the moment tensor components and the recorded waveforms. The L1 norm is used as an optimum solution criterion, therby allowing first motions to be included in the data set. A mixed data set is warranted when only a small number of amplitude measurements are available. Displacement amplitudes at the recording stations are estimated by seismogram modeling in the case of the shallow earthquake and by the application of an optimum lag inverse filter in the case of the deep earthquake. The inverse filter is designed to remove the combined effects of the recording system and signal distortion owing to anelasticity. Long-period P waves from an intraplate earthquake located between the Caribbean arc and the mid-Atlantic ridge at a depth of 25 km reveal a source with a moment time functin in the far field that has rise and fall times of 2¿1 s. By implication the duration of faulting was short in comparison with shallow earthquakes of similar size at active plate margins. Approximately 89% of the total moment of 0.8¿1025 dyn cm pertains to a change in deviatoric stress, which is represented almost totally by a double couple. A 20% increase in the double couple component was achieved by a sysematic steepening by 5 ¿--8 ¿ of takeoff angles for ray paths to teleseismic distances computed from the Herrin travel times. A submoho source depth is assumed, consistent with generally accepted models of oceanic lithosphere. The double couple component from the moment tensor is similar to the first motion solution but is dominated by a strike-slip rather than a dip-slip radiation pattern. Amplitudes and first motion polarities from a deep earthquake beneath the Bonin arc yield a moment tensor that is 72% double couple and 19% compensated linear vector dipole. A similar steepening of the ray paths in this case consistent with a 7% reduction in the compressional velocity at the source depth results in a double couple component of more than 90%. Lateral heterogeneity in the source region precludes a simple interpretation of this apparent velocity reduction. Our results demonstrate that the inversion of body wave amplitude data for the unconstained moment tensor can yield essentially pure double couples.