A data processing system 2 utilises a register renaming mechanism 10, 26 to rename architectural register specifiers to physical register specifiers to facilitate out-of-order processing. The register renaming mechanism 10, 26 includes a renaming recovery unit 26 which enables recovery from incorrectly executed speculative instructions by restoring the register mapping to the state prior to those incorrect instructions with the physical registers restored to containing the data values which were current at the time prior to that incorrect instruction. In the case of load instructions, these are treated as speculative but the data value returned in response to the load instruction and stored within a physical register is released for use as soon as it is returned and prior to a determination result being available as to whether or not that data value is corrupt. Corruption checking an take the form of ECC checking, parity checking and the like, and when a late error signal is generated then this indicates whether or not the data value has been properly released for use. If corruption is detected, then the renaming recovery unit 26 is used to recover the state of the system 2 in a precise way to that preceding the failing load instruction.