A method, system, and processor chip design for reducing the latency between completing a LARX operation and receiving the associated STCX operation to complete the update to the cache line. Each entry of the store queue of the issuing processor is provided an additional tracking bit (priority bit). The priority bit is set whenever a STCX operation is placed within the entry. During selection of an entry for dispatch by the arbitration logic, the arbitration logic scans the value of the priority bits of each eligible entry. An entry with the priority bit set is given priority in the selection process within architectural rules. That entry is then selected for dispatch as early as is possible within the established rules.