A space allocator in a file management system maintains and uses one or more offsets and a stored value of the largest space skipped on previous scans to increase the efficiency of scans for available space in a file system space map. When the space allocator determines a current allocation request is greater than the largest space skipped in the previous scan, a last allocated offset can be used to begin scanning to reduce the portion of the map to scan in order to find available space. When the space allocator determines the current allocation request is less than or equal to the largest space skipped in the previous scan, a first available offset can be used to begin scanning for an appropriate unused space.