Abstract: A processor interleaves instructions according to a priority rule which determines the frequency with which instructions from each respective thread are selected and added to an interleaved stream of instructions to be processed in the data processor. The frequency with which each thread is selected according to the rule may be based on the priorities assigned to the instruction threads. A randomization is inserted into the interleaving process so that the selection of an instruction thread during any particular clock cycle is not based solely by the priority rule, but is also based in part on a random or pseudo random element. This randomization is inserted into the instruction thread selection process so as to vary the order in which instructions are selected from the various instruction threads while preserving the overall frequency of thread selection (i.e. how often threads are selected) set by the priority rule.