1. A method of rebuilding data stored on a dispersed data storage network comprising a plurality of networked computers including a plurality of slice servers, each of said slice servers storing a plurality of data slices, each of said data slices being identified by a data slice identifier, whereby n of said data slices are associated with a corresponding data segment, and whereby m of said associated data slices are required to reconstruct said corresponding data segment, and further whereby m is less than n−1, said method comprising the steps of: receiving a message from one of said networked computers, said message indicative of the inaccessibility of a plurality of data slices; adding data slice identifiers identifying said plurality of data slices to a list of data slices to be rebuilt; for each data slice identified by said list of data slices to be rebuilt: determining a corresponding data segment; reading at least m data slices associated with said corresponding data segment, said at least m data slices not identified on said list of data slices to be rebuilt; 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 multiplying the reconstructed coded matrix by a decoding matrix in accordance with an information dispersal algorithm to reconstruct the data segment; encoding the reconstructed data segment by arranging data words of the reconstructed data segment into a data matrix and multiplying the data matrix by the encoding matrix in accordance with the information dispersal algorithm to produce a coded matrix that is arranged into a new plurality of data slices; writing one of the new plurality of data slices to one of said plurality of slice servers to rebuild said data slice identified by said list of data slices to be rebuilt.