1. A method for execution by a computing device, the method comprises: determining, by the computing device, whether to send an encoded data slice of a set of encoded data slices in accordance with a zero information gain (ZIG) format, wherein data is encoded using a dispersed storage error coding function to produce the set of encoded data slices, and wherein the data can be recreated from a decode threshold number of encoded data slices of the set of encoded data slices; when the encoded data slice is to be sent in accordance with the ZIG format: selecting a partial encoding threshold number of encoded data slices of the set of encoded data slices, wherein the partial encoding threshold number of encoded data slices does not include the encoded data slice; and generating a set of ZIG encoded data slices based on a ZIG function and the partial encoding threshold number of encoded data slices, wherein the set of ZIG encoded data slices represents recovery information of the encoded data slice and wherein generating a ZIG encoded data slice of the set of ZIG encoded data slices includes: generating a decoding matrix for the encoded data slice based on an encoding matrix of the dispersed storage error coding function; and generating the ZIG encoded data slice based on the decoding matrix and on a first encoded data slice of the partial encoding threshold number of encoded data slices; and outputting the set of ZIG encoded data slices.