We investigate the exploration of an unknown environment when no reward function is provided. Building on the incremental exploration setting introduced by Lim and Auer , we define the objective of learning the set of ε-optimal goal-conditioned policies attaining all states that are incrementally reachable within L steps (in expectation) from a reference state s0. In this paper, we introduce a novel model-based approach that interleaves discovering new states from s0 and improving the accuracy of a model estimate that is used to compute goal-conditioned policies to reach newly discovered states. The resulting algorithm, DisCo, achieves a sample complexity scaling as Õ(L5SL + ε ΓL + ε A ε-2), where A is the number of actions, SL + ε is the number of states that are incrementally reachable from s0 in L + ε steps, and ΓL + ε is the branching factor of the dynamics over such states. This improves over the algorithm proposed in  in both ε and L at the cost of an extra ΓL+ ε factor, which is small in most environments of interest. Furthermore, DisCo is the first algorithm that can return an ε/cmin-optimal policy for any cost-sensitive shortest-path problem defined on the L-reachable states with minimum cost cmin. Finally, we report preliminary empirical results confirming our theoretical findings.