1. A method comprises: encoding data using a dispersed storage error coding function to produce a set of encoded data slices, wherein the data is re-creatable from a decode threshold number of encoded data slices of the set of encoded data slices; generating a zero information gain (ZIG) encoded data slice that represents a component of recovery information of a first encoded data slice of the set of encoded data slices using a ZIG function and a second encoded data slice of the set of encoded data slices; and outputting the ZIG encoded data slice and a subset of encoded data slices of the set of encoded data slices, wherein the subset of encoded data slices includes less than the decode threshold number of encoded data slices and does not include the first or the second encoded data slice.