A storage reorganizing system subdivides a reorganizable storage space into tile areas. Each tile area either contains file data or does not contain file data. The data in a tile area that contains file data is referred to as a tile. A tile area that does not contain file data is referred to as a vacancy. Tiles that are not yet located in their goal positions, as defined by a recorded goal state definition, are opportunistically moved to available vacancies that are the goal positions for such tiles as the vacancies become available. Each tile move leaves behind it a new vacancy. The speed of opportunistic tile moving is optimized by first locating the largest vacancies that are each to be filled with the largest amount of tile data and by first moving tiles to such vacancies. One goal state produces a defragmented set of files. Another goal state produces an intentionally fragmented set of files. A third goal state produces a set of files that are fragmented and whose fragments are tightly interleaved on an access-wise basis so as to enable quick switching between a fragment of a first file and a fragment of a second file.