1. A method comprises: encoding data segments of data into a plurality of sets of encoded data slices in accordance with first error coding dispersal storage function parameters, wherein the data includes non-priority data portions and priority data portions, wherein data boundaries of the non-priority data portions and priority data portions are not aligned with boundaries of the data segments; determining priority data segments of the data segments, wherein one of the priority data segments includes at least a fraction of one of the priority data portions; redundantly encoding the priority data segments in accordance with second error coding dispersal storage function parameters to produce sets of priority encoded data slices, wherein the first error coding dispersal storage function parameters prioritize data recovery speed over data recovery reliability and the second error coding dispersal storage function parameters prioritize data recovery reliability over data recovery speed, wherein a substantially identical representation of a pre-encoded priority data segment of the priority data segments is recoverable from a corresponding set of the plurality of sets of encoded data slices or from a corresponding set of the sets of priority encoded data slices; and outputting the plurality of sets of encoded data slices and the sets of priority encoded data slices to a dispersed storage network (DSN) memory for storage therein.