A processor and data processing system suitable for dispatching an instruction to an issue unit. The issue unit includes a primary issue queue and a secondary issue queue. The instruction is stored in the primary issue queue if the instruction is currently eligible to issue for execution. The instruction is stored in the secondary issue queue if the instruction is currently ineligible to issue for execution. An instruction may be moved from the primary issue queue to the secondary issue queue if instruction is dependent upon results from another instruction. In one embodiment, the instruction may be moved from the primary issue queue to the secondary issue queue after issuing the instruction for execution. In this embodiment, the instruction may be maintained in the secondary issue queue for a specified duration. Thereafter, the secondary issue queue entry containing the instruction is deallocated if the instruction has not been rejected.