A dispersed storage system includes a plurality of storage units that each include a partial rebuild grid module. The partial rebuild grid module includes partial rebuilding functionality to reconstruct one of a plurality of encoded data slices wherein the plurality of encoded data slices are generated from a data segment based on an error encoding dispersal function. In the partial rebuilding process, a data slice is rebuilt by combining in any order slice partials generated from at least a threshold number T of the plurality of data slices.