In this paper, we propose an interactive approach to determine a compromise solution in the multicriteria spanning tree problem. We assume that the Decision Maker’s preferences over spanning trees can be represented by a weighted sum of criteria but that weights are imprecisely known. In the first part of the paper, we propose a generalization of Prim’s algorithm to determine the set of possibly optimal tradeoffs. In the second part, we propose an incremental weight elicitation method to reduce the set of feasible weights so as to identify a necessary optimal tradeoff. Numerical tests are given to demonstrate the practical feasibility of the approach.