We demonstrate a volumetric random laser with an optical efficiency of 15%. We use a 1.33 mol% Nd:YVO4 crystal, grind it and mix the particles into ten different size distributions with mean particle sizes ranging from approximately 10 micrometers to 100 micrometers. After pressing into pellets, each of the ten groups has its transport mean free path calculated from the distribution spectra and experimentally measured by means of its backscattering cone. We then calculate the fill fractions of each sample. The pellets are diode-pumped at 806.5 nm. Linewidth narrowing and output power are measured as a function of absorbed pump power. We demonstrate that the smaller particles, trapped between large particles, serve as gain centers whereas the large particles control the light diffusion into the sample. By optimizing diffusion and gain we achieve high slope efficiency.