k- and t-optimality algorithms [9, 6] provide solutions to DCOPs that are optimal in regions characterized by its size and distance respectively. Moreover, they provide quality guarantees on their solutions. Here we generalise the k- and t-optimal framework to introduce C-optimality, a flexible framework that provides reward-independent quality guarantees for optima in regions characterised by any arbitrary criterion. Therefore, C-optimality allows us to explore the space of criteria (beyond size and distance) looking for those that lead to better solution qualities. We benefit from this larger space of criteria to propose a new criterion, the socalled size-bounded-distance criterion, which outperforms kand t-optimality. Categories and Subject Descriptors I.2.11 [Artificial Intelligence]: Distributed AI General Terms Algorithms, Design, Theory Keywords DCOP, approximate algorithm, bound, region optimality