A data processing apparatus and method are provided for implementing a replacement scheme for entries of a storage unit. The data processing apparatus has processing circuitry for executing multiple program threads including at least one high priority program thread and at least one lower priority program thread. A storage unit is then shared between the multiple program threads and has multiple entries for storing information for reference by the processing circuitry when executing the program threads. A record is maintained identifying for each entry whether the information stored in that entry is associated with a high priority program thread or a lower priority program thread. Replacement circuitry is then responsive to a predetermined event in order to select a victim entry whose stored information is to be replaced. To achieve this, the replacement circuitry performs a candidate generation operation to identify a plurality of randomly selected candidate entries, and then references the record in order to preferentially select as the victim entry a candidate entry whose stored information is associated with a lower priority program thread. This improves the performance of the high priority program thread(s) by preferentially evicting from the storage unit entries associated with lower priority program threads.