1. A computing device comprising: an interface configured to interface and communicate with a dispersed storage network (DSN); memory that stores operational instructions; and a processing module operably coupled to the interface and to the memory, wherein the processing module, when operable within the computing device based on the operational instructions, is configured to: determine whether a number of pluralities of unique pillar combinations of at least read threshold number of encoded data slices (EDSs) supported by pluralities of EDSs associated respectively with a data object compares favorably with a threshold number, wherein the pluralities of EDSs are distributedly stored across a plurality of storage units (SUs) within the DSN, wherein the data object is segmented into a plurality of data segments, wherein a data segment of the plurality of data segments is dispersed error encoded in accordance with first dispersed error encoding parameters to produce a set of EDSs, wherein the read threshold number of EDSs provides for reconstruction of the data segment, and wherein a write threshold number of EDSs provides for a successful transfer of the set of EDSs from a first at least one storage location in the DSN to a second at least one storage location in the DSN; when the number of pluralities of unique pillar combinations of the at least read threshold number of EDSs supported by the pluralities of EDSs associated respectively with the plurality of data segments of the data object compares unfavorably with a unique pillar combination number: dispersed error encode each data segment of the plurality of data segments in accordance with second dispersed error encoding parameters to generate additional pluralities of EDSs associated respectively with the data object, wherein the additional pluralities of EDSs support additional unique pillar combinations of the at least read threshold number of EDSs; and distributedly store the additional pluralities of EDSs associated respectively with the data object across the plurality of SUs within the DSN to support the additional unique pillar combinations of the at least read threshold number of EDSs.