Predicting memory instruction punts in a computer processor using a punt avoidance table (PAT) are disclosed. In one aspect, an instruction processing circuit accesses a PAT containing entries each comprising an address of a memory instruction. Upon detecting a memory instruction in an instruction stream, the instruction processing circuit determines whether the PAT contains an entry having an address of the memory instruction. If so, the instruction processing circuit prevents the detected memory instruction from taking effect before at least one pending memory instruction older than the detected memory instruction, to preempt a memory instruction punt. In some aspects, the instruction processing circuit may determine, upon execution of a pending memory instruction, whether a hazard associated with the detected memory instruction has occurred. If so, an entry for the detected memory instruction is generated in the PAT.