The method of specifying the amplitudes of teleseismic phases (P, pP, and sP, or three-component direct S) used in the relative amplitude moment tensor method (Pearce and Rogers, 1989) is modified to provide for a most likely, or ''best fit,'' moment tensor. Instead of imposing uniform probability on all amplitudes lying between upper and lower bounds which are specified for each phase, a Gaussian probability function related to these bounds is assumed. This modification acknowledges that an amplitude value nearer to the midpoint of the range is more likely to represent the true value, and results in a probability density function in moment tensor space which is itself peaked, yielding s single most likely solution. By contrast, a uniform likelihood within specified amplitude bounds can yield only a range of solutions acceptable with uniform likelihood. This Gaussian relative amplitude method (GRAM) is applied to several earthquakes previously studied using the original procedure (relative amplitude moment tensor program, RAMP). GRAM yields results which agree closely with those of RAMP, but in which the source type is more tightly defined, particularly in its deviatoric component. Previously, any single solution had to be chosen arbitrarily from near the centroid of the compatible range, but it is shown that, as expected, the most likely solution may lie anywhere within this range. ¿ American Geophysical Union 1992