Memory caches are critical components of modern web services that improve response times and reduce the load on backend databases. In multi-tenant clouds, several instances of caches compete for memory. The current state-of-the-art is to statically allocate memory for cache instances (e.g., based on cost-tier) but such allocation tends to be sub-optimal as memory demands of instances often vary with time and not known apriori. We propose MemSweeper, which dynamically manages memory between cache instances. MemSweeper uses a novel, score-based metric and an associated algorithm to identify cache instances whose working sets fit well within their allocated memory and thus can relinquish a portion of the memory without suffering appreciable loss in their hit rates. Using a combination of synthetic and production traces on a real implementation, we show that MemSweeper achieves 74% improvement (on average) in the miss rate of critical tenants without degrading the performance of other tenants.