In a file server, a file system is built upon a volume of data storage. The file system includes multiple cylinder groups. Each cylinder group includes file system blocks. The file system blocks include allocated blocks and free blocks. The volume includes slices of storage, and each slice stores at least one of the cylinder groups. A hierarchical slice map has a top level that includes a count of free blocks in the file system, an upper level that includes a count of free blocks in groups of the slices, an intermediate level that includes a count of the free blocks in sub-groups of the slices, and a bottom level that includes a count of the free blocks in each slice of storage. To find a free block for allocation to a file, the slice map hierarchy is searched in a top-down fashion.