1. A method for execution by one or more computers associated with a dispersed data storage network, the method comprises: identifying a data slice requiring rebuilding to produce an identified data slice, wherein the identified data slice is one of a set of data slices that constitute a data segment, wherein data words of the data segment are arranged into a data matrix that is encoding using an encoding matrix function in accordance an information dispersal algorithm to produce a coded matrix of coded values that is arranged into the set of data slices; retrieving at least m number of data slices for the set of data slices, wherein n represents the number of data slices in the set of data slices and m is less than or equal to n−2; decoding the retrieved at least m number of data slices by arranging coded values of the retrieved at least m number of data slices into a reconstructed coded matrix and decoding the reconstructed coded matrix using a decoding matrix function in accordance with the information dispersal algorithm to reconstruct the data segment; encoding the reconstructed data segment by arranging data words of the reconstructed data segment into the data matrix and encoding the data matrix using the encoding matrix function in accordance with the information dispersal algorithm to produce the coded matrix that is arranged into a new set of data slices; selecting a data slice of the new set of data slices as a rebuilt data slices to replace the identified data slice; and outputting the rebuilt data slice for storage in one of a plurality of data slice servers.