A common way of characterizing minimax estimators in point estimation is by moving the problem into the Bayesian estimation domain and finding a least-favorable distribution. The Bayesian estimator induced by a least-favorable prior, under mild conditions, is then known to be minimax. However, finding least favorable distributions can be challenging due to inherent optimization over the space of probability distributions, which is infinite-dimensional. This paper develops a dimensionality reduction method that allows us to move the optimization to a finite-dimensional setting with an explicit bound on the dimension. The benefit of this dimensionality reduction is that it permits one to use popular algorithms such a gradient descent to find least-favorable distributions. Throughout the paper, in order to make progress on the problem, we restrict ourselves to the Bayesian risks induced by a relatively large class of loss functions, namely Bregman divergences.