A technique for restoring a register renaming map is described. In one example, a restore table having a number of storage locations saves a copy of the register renaming map whenever a flow-risk instruction is passed to a re-order buffer. When all storage locations are full, further instructions still pass to the re-order buffer, but a copy of the map is not saved. A storage location subsequently becomes available when its associated flow-risk instruction is executed. A register renaming map state for an unrecorded flow-risk instruction passed to the re-order buffer whilst the storage locations were full is generated and stored in the available location. This is generated using the restore table entry for a previous flow-risk instruction and re-order buffer values for intervening instructions between the previous and unrecorded flow-risk instructions. The restore table can be used to restore the map if an unexpected change in instruction flow occurs.