1. A method that is executed by one or more processing modules of one or more computing devices, the method comprises: encoding a data segment of data using a dispersed storage error coding function to produce a write threshold number of encoded data slices; identifying, by a distributed storage and task (DST) processing unit which of a plurality of primary storage units is available for storing the write threshold number of encoded data slices; for those primary storage units of the plurality of primary storage units that are available, issuing a write slice request that includes a slice name corresponding to each of the available primary storage units and an encoded data slice corresponding to each of the available primary storage units; for those primary storage units of the plurality of primary storage units that are unavailable, selecting a storage approach for storing an encoded data slice associated with the unavailable primary storage units; for each of the primary storage units of the primary storage units that are unavailable, further selecting a foster storage unit in accordance with the selected storage approach; and issuing a write imposter slice request to each selected foster storage unit, wherein the request includes a slice name corresponding to the selected foster storage unit and an imposter encoded data slice corresponding to an unavailable primary storage unit.