Methods are described which extend the usefulness of a previously published method for determining the mass absorption coefficient (μ) by means of Compton scattering. The original method was restricted to (1) rocks and minerals of intermediate atomic number, and (2) analysis of trace elements whose analytical line is of shorter wavelength than that of the absorption edge of the heaviest matrix element. Mass absorption coefficients can be determined for low atomic number matrices by the use of a long wavelength primary radiation, such as CrKα (Ryland, 1964). Values of μ for high atomic number matrices can be measured if a yttrium oxide filter is used to absorb interfering MoKα radiation. The relation between μ at 0.9A and the reciprocal intensity of the Compton-scattered MoKα indicates that μ values can be measured, with an error of less than 3 percent, for materials whose mean atomic number is as high as CuO. Appropriate values for μ can be computed for regions on the long wavelength sides of major element absorption edges by the use of a series of simultaneous equations in terms of (1) the mass absorption coefficient at 0.9A, (2) the intensities of the Kα lines of the matrix elements, (3) published data on the rate of change of μ, for each matrix element, with respect to wavelength, and (4) the major element analysis of a standard. Data are given for Fe, Mn, Ti, and V in several different matrices. Overall errors appear to be positive, and amount to 2 to 10 percent.