1. A method comprises: establishing, by a processing module of a dispersed storage unit, an address based memory balancing scheme that is based on allocating a set of unique address ranges to a set of memory devices of the dispersed storage unit, wherein a respective unique address range is allocated to a respective memory device of the set of memory devices, in which the respective unique address range corresponds to a slice name range, and wherein the slice name range pertains to slice names of a plurality of data slices that are created when encoding a plurality of data segments, in which for a respective data segment, n data slices are generated in accordance with an error coding function, and in which at least a threshold number k of the n data slices are needed to reconstruct the respective data segment, where k is less than n; storing, in a first memory device of the set of memory devices, encoded data slices having slice name range in accordance with a first unique address range; storing, in a second memory device of the set of memory devices, encoded data slices having slice name range in accordance with a second unique address range; identifying a memory loading mismatch between the first memory device and the second memory device, wherein the memory loading mismatch occurs when more storage space is utilized in the first memory device than utilized in the second memory device for storing the encoded data slices; determining an estimated impact to reduce the memory loading mismatch; and when the estimated impact compares favorably to an impact threshold, modifying the first and second sets of unique address ranges based on the memory loading mismatch, by reducing the first unique address range corresponding to the first memory device and expanding the second unique address range corresponding to the second memory device, such that storage space utilization of the first and second memory devices is approximately balanced for the first and second unique address ranges.