Management of a nonvolatile medium, such as a flash memory, is disclosed. The nonvolatile medium can be organized as a plurality of storage units. The storage units used to store user data in the form of logical units (sectors). For purposes of read disturb handling, the logical units need to be copied out of the storage unit and thus invalidated prior to hitting a read disturb limit. Rather than waiting until the read disturb limit is reached and copying out all of the logical units at once, the logical units are moved gradually over a period of time based, in part, on a number of valid logical units. A number of reads can also be used to determine when logical units are moved. Distributed movement of the logical units avoids an avalanche effect wherein multiple logical units need to be moved at once, which slows the overall system.