Multiple data slices are generated from an original data segment. The data slices are constructed to prevent recovery of the original data segment using a single related data slice, but to allow recovery of the original data segment using fewer than all of the data slices. Each data slice is stored in the same memory stripe as the other data slices. The memory stripe extends across multiple memory devices and multiple different distributed storage units. The memory device in which each data slice is stored can be determined based on a source name associated with each data slice.