1. A method for storing error coded data slices in a dispersed storage network (DSN), wherein a data segment is encoded using an error coding dispersed storage function to produce a plurality of error coded data slices, wherein each of the plurality of error coded data slices has a unique slice name, and wherein each of the unique slice names includes a common source name and unique addressing information, the method comprising: receiving, by a first dispersed storage unit of the DSN, a first error coded data slice of a plurality of error coded data slices and the unique slice name of the first error coded data slice; performing, by the first dispersed storage unit, a deterministic function on the common source name of the unique slice name of the first error coded data slice to select a memory device of a plurality of memory devices of the first distributed storage unit; and storing, by the first dispersed storage unit, the first error coded data slice in the memory device of the plurality of memory devices of the first dispersed storage unit based on the unique slice name of the first error coded data slice; receiving, by a second dispersed storage unit of the DSN, a second error coded data slice of a plurality of error coded data slices and the unique slice name of the second error coded data slice; performing, by the second dispersed storage unit, the deterministic function on the common source name of the unique slice name of the second error coded data slice to select a memory device of a plurality of memory devices of the second distributed storage unit; and storing, by the second dispersed storage unit, the second error coded data slice in the memory device of the plurality of memory devices of the second dispersed storage unit based on the unique slice name of the second error coded data slice.