In this paper, we investigate the problem of eliciting information from an expert, where the assumed uncertainty model is a coherent upper prevision (or equivalently a closed convex set of probabilities). The goal is to solve a decision problem under the maximality decision rule, with as few queries to the expert as possible. To address this, we study the range of coherent upper bounds an expert may give on a given query. In doing so, we provide new results and characterisations for this range. We then use these results to provide an algorithm of elicitation. We illustrate the algorithm on an example.