Building Bayesian belief networks in the absence of data involves the challenging task of eliciting conditional probabilities from experts to parameterize the model. In this paper, we develop an analytical method for determining the optimal order for eliciting these probabilities. Our method uses prior distributions on network parameters and a novel expected proximity criteria, to propose an order that maximizes information gain per unit elicitation time. We present analytical results when priors are uniform Dirichlet; for other priors, we find through experiments that the optimal order is strongly affected by which variables are of primary interest to the analyst. Our results should prove useful to researchers and practitioners involved in belief network model building and elicitation.