A mixture of polymer with high dielectric constant filler has appeal as a high energy density capacitor dielectric. However, at "low" volume fractions of filler, the primary effect of a high dielectric constant filler (relative to the polymer matrix) is to increase the field in the matrix rather than store energy in the filler. Below a threshold concentration, which depends on particle aspect ratio, little advantage can be gained from a high dielectric filler. Above this threshold concentration, the energy density increases rapidly with volume fraction of filler. We have examined this problem through 3D finite element computations for random dispersions of spherical particles from 0 to 45% volume fraction and for random dispersions of prolate spheroidal particles with an aspect ratio of 3 from 0 to 27% and in both cases for dielectric contrasts from 3 to 3000 in a 1,3,10 sequence.