1. A storage integrity processing unit in a dispersed storage network, comprises: a network interface for interfacing with a plurality of storage units in the distributed storage network; and a grid module including: a rebuild agent operably coupled to: receive an identification of an identified data slice of a data segment that requires rebuilding from a corresponding one of the plurality of storage units, wherein the data segment is encoded using an error encoding dispersal function to generate an encoded data segment, wherein portions of the encoded data segment are interleaved into a number X of a plurality of encoded data slices for storage in the plurality of storage units and wherein the identified data slice is one of the number X of the plurality of encoded data slices; and retrieve at least a number T of the plurality of encoded data slices from the plurality of storage units, wherein the number T corresponds to a threshold number of the number X of the plurality of encoded data slices needed to reconstruct the data segment based on the error encoding dispersal function, wherein the number T equals less than the number X; and a rebuild module operably coupled to reconstruct the data segment from at least the number T of the plurality of encoded data slices to produce a reconstructed data segment by decoding at least the number T of the plurality of encoded data slices using a decoding matrix A in accordance with the error encoding dispersal function; and generate a rebuilt encoded data slice corresponding to the identified data slice from the reconstructed data segment using the error encoding dispersal function.