The paper introduces the notion of freely completable partial solutions to characterize constraint satisfaction problems that have components which are relatively easy to solve and are only loosely connected to the remaining parts of the problem. Discovering such partial solutions during the solution process can result in strongly pruned search trees. We give a general definition of freely completable partial solutions, and then apply it to resource-constrained project scheduling. In this domain, we suggest a heuristic algorithm that is able to construct freely completable partial schedules. The method - together with symmetry breaking applied before search - has been successfully tested on real-life resource-constrained project scheduling problems containing up to 2000 tasks.