1. A method of rebuilding data on a dispersed data storage network, said method comprising the steps of: identifying, by a computer of the dispersed data storage network, a data segment that has at least one data slice requiring rebuilding, wherein the data segment is encoded in accordance with an information dispersal algorithm to produce a set of data slices that are stored on slice servers of the dispersed data storage network, wherein the set of data slices are different from one another and includes the at least one data slice requiring rebuilding, wherein the at least one slice requiring rebuilding is a subset of the set of data slices, wherein the at least one data slice that requires rebuilding from the data segment is identified based on one or more of: determining that the at least one data slice requiring rebuilding is outdated with respect to other data slices of the set of data slices; determining that the at least one data slice requiring rebuilding is missing; determining that the at least one data slice requiring rebuilding is corrupted; determining that the at least one data slice requiring rebuilding failed a read operation; determining that the at least one data slice requiring rebuilding failed a write operation; requesting, by the computer from at least some of the slice servers, at least a reconstruction number of data slices of the set of data slices, wherein the at least a reconstruction number of data slices does not include the at least one data slice requiring rebuilding; reconstructing, by the computer, the data segment from the at least a reconstruction number of data slices to produce a reconstructed data segment; encoding, by the computer, the reconstructed data segment in accordance with the information dispersal algorithm to reproduce the set of data slices including at least one new data slice that corresponds to the at least one data slice that requires rebuilding; and writing, by the computer, the at least one new data slice to one or more of the slice servers such that a full set of data slices are stored in the slice servers for the data segment.