Embodiments of the present invention are directed to methods, and distributed data-storage systems employing the methods, for recovering redundancy within a distributed data-storage system upon failure of one or more mass-storage devices within a component data-storage system of the distributed data-storage system. In certain embodiments, failure of a mass-storage device within a component data-storage system elicits a redundancy-recovery operation in which segments affected by the mass-storage-device failure or failures are moved, by a process referred to as "migration," to other component data-storage systems of the distributed data-storage system, and are recovered as a by-product of migration. Certain embodiments of the present invention more efficiently address redundancy recovery by moving only as many segments from the component data-storage system as needed to provide sufficient free space within the component data-storage system to recover the remaining segments affected by the mass-storage-device failure or failures within the component data-storage system.