A method is described which uses the relative amplitudes of related seismic phases to improve constraints on the form of the P and S wave radiation patterns, from which a moment tensor determination is obtained complete with a well-founded measure of its precision. Two types of teleseismic relative amplitude measurements may be employed: those relating P, pP, and sP and those relating the three components of the direct S wave. Examples are given which apply the method to (1) smaller shallow earthquakes (mb~5.8) using long-period seismograms, and (3) large mb shallow earthquakes, which require both P and S wave data at long period. The relative amplitude moment tensor program (RAMP) is an advance on the relative amplitude method of Pearce <1977, 1980> in that the a priori double couple assumption is now relaxed. Results are compared with those of other moment tensor methods where available. RAMP is found to be a sensitive indicator of volumetric source component even for small data sets, for which it is less good at discriminating between different constant-volume source types, notably the double couple and the compensated linear vector dipole. Since current inverse methods presume a constant-volume source, our method alone is a reliable indicator of volumetric component, which is important for the analysis of source processes and in earthquake-explosion discrimination. ¿ American Geophysical Union 1989