1. A method for use in a distributed storage processing unit, the method comprising: generating a first plurality of data slices including different encoded versions of a first data portion; generating a second plurality of data slices including different encoded versions of a second data portion; and sending the first plurality of data slices and the second plurality of data slices to be stored concurrently in different storage sets, each of the different storage sets including a plurality of distributed storage units different from the distributed storage units included in others of the different storage sets; at least a read threshold number of data slices from a first storage set required to reconstruct the first data portion; and at least a read threshold number of data slices from a second storage set required to reconstruct the second data portion.