The Monte Carlo calculation of dose for radiotherapy treatment planning purposes introduces unavoidable statistical noise into the prediction of dose in a given volume element (voxel). When the doses in these voxels are summed to produce dose volume histograms (DVHs), this noise translates into a broadening of differential DVHs and correspondingly flatter DVHs. A brute force approach would entail calculating dose for long periods of time--enough to ensure that the DVHs had converged. In this paper we introduce an approach for deconvolving the statistical noise from DVHs, thereby obtaining estimates for converged DVHs obtained about 100 times faster than the brute force approach described above. There are two important implications of this work: (a) decisions based upon DVHs may be made much more economically using the new approach and (b) inverse treatment planning or optimization methods may employ Monte Carlo dose calculations at all stages of the iterative procedure since the prohibitive cost of Monte Carlo calculations at the intermediate calculation steps can be practically eliminated.