Clusters provide powerful computing environments, but in prac-tice much of this power goes to waste, due to the static allocation of tasks to nodes, regardless of their changing computational re-quirements. Dynamic consolidation is an approach that migrates tasks within a cluster as their computational requirements change, both to reduce the number of nodes that need to be active and to eliminate temporary overload situations. Previous dynamic consol-idation strategies have relied on task placement heuristics that use only local optimization and typically do not take migration over-head into account. However, heuristics based on only local opti-mization may miss the globally optimal solution, resulting in un-necessary resource usage, and the overhead for migration may nul-lify the benefits of consolidation. In this paper, we propose the Entropy resource manager for ho-mogeneous clusters, which performs dynamic consolidation based on constraint programming and takes migration overhead into ac-count. The use of constraint programming allows Entropy to find mappings of tasks to nodes that are better than those found by heuristics based on local optimizations, and that are frequently globally optimal in the number of nodes. Because migration over-head is taken into account, Entropy chooses migrations that can be implemented efficiently, incurring a low performance overhead.