1. A method comprises: segmenting, by a dispersed storage (DS) processing module, a data object into data segments; encoding, by the dispersed storage (DS) processing module and in accordance with a dispersed storage error encoding function, the data segments to produce a plurality of encoded data slices including slice names; outputting, by the DS processing module, the plurality of encoded data slices to storage units of a dispersed storage network (DSN); receiving, by one of the storage units, an encoded slice of the plurality of encoded slices; determining, by the one of the storage units, whether the received encoded slice is to be sub-sliced using a sub-slicing error encoding function upon receiving a command to generate a plurality of encoded sub-slices; when the encoded slice is to be sub-sliced, encoding, by the one of the storage units and in accordance with the sub-slicing error encoding function, the encoded slice to produce a plurality of encoded sub-slices; and outputting, by the one of the storage units, the plurality of encoded sub-slices to a set of storage units.