A method, a system and a computer program product for handling speculative stores. The system determines when a speculative store buffer is not full. An indicator is generated when the speculative store buffer is not full, and the speculative stores are input into the speculative store buffer. When the speculative store buffer is full, a full buffer indicator is generated. Speculative stores prevented from entering the speculative store buffer are overflow stores. The overflow list is searched to determine whether one or more addresses of the overflow stores are present in the overflow list. When one or more addresses of the overflow stores are not present in the overflow list, the overflow stores are stored in the overflow list.