With the trend towards multi-core processors, support for multi-threaded programming is increasingly important. We are interested in providing development and deployment options to allow programmers to select minimal locks, achieving maximal concurrency, at different levels of granularity within a composite system. We explore local properties of the fixpoint lattice of a Galois connection between exclusion requirements and concurrency potential of a composite object. This allows us to develop incremental algorithms for lock selection. Implemented within integrated development environments, such algorithms will allow programmers to interactively select minimal locks with safety.