1. A method for execution by one or more computers associated with a dispersed data storage network, the method comprises: identifying, by a first rebuilder application operating on a first slice server, a data slice having a storage error; identifying, by the first rebuilder application or by a second rebuilder application operating on the second slice server, a data segment based on the identified data slice, wherein the data segment was encoded in accordance with an information dispersal function to produce a set of data slices, which includes the identified data slice; identifying, by the second rebuilder application operating on the second slice server, one or more other slice servers that are storing other data slices of the set of data slices; retrieving, by the second rebuilder application operating on the second slice server from the one or more other slice servers, a sufficient number of the other data slices to reconstruct the data segment; decoding, by the second rebuilder application operating on the second slice server, the sufficient number of the other data slices in accordance with the information dispersal function to reconstruct the data segment; encoding, by the second rebuilder application operating on the second slice server, the reconstructed data segment in accordance with the information dispersal algorithm to produce a new set of data slices; and selecting, by the second rebuilder application operating on the second slice server, a data slice of the new set of data slices as a rebuilt data slice of the identified data slice.