A method begins by a dispersed storage (DS) processing module determining whether to send an encoded data slice of set of encoded data slices in accordance with a zero information gain (ZIG) format. When the encoded data slice is to be sent in accordance with the ZIG format, the method continues with the DS processing module 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. The method continues with the DS processing module outputting the set of ZIG encoded data slices.