Accessing at least one memory location by one of a plurality of transactions in a multi-processor transactional execution environment is provided. Included is assigning, by a computer system, a conflict priority to a transaction; based on encountering a conflict with another process for a memory location, comparing, by the computer system, the assigned conflict priority of the transaction with another priority of the another process; and based on the conflict priority of the transaction being the higher priority continuing the transaction; and based on the conflict priority of the transaction being the lower priority, aborting the transaction.