A log structured store uses a single write I/O for a number of diverse and non-contiguous pages within a large buffer instead of using a write I/O for each page separately. This requires that pages be relocated on every write, because pages are never updated in place. Instead, pages are dynamically remapped on every write. Log structuring was invented for and used initially in file systems. Today, a form of log structuring is used in SSD controllers because an SSD requires the erasure of a large block of pages before flash storage can be reused. No update-in-place requires that the storage for out-of-date pages be reclaimed (garbage collected or "cleaned"). We analyze cleaning performance and introduce a cleaning strategy that uses a new way to prioritize the order in which stale pages are garbage collected. Our cleaning strategy approximates an "optimal cleaning strategy". Simulation studies confirm the results of the analysis. This strategy is a significant improvement over previous cleaning strategies.