A data processing system includes a memory subsystem and an execution unit, coupled to the memory subsystem, which executes store instructions to determine target memory addresses of store operations to be performed by the memory subsystem. The data processing system further includes a mode field having a first setting indicating strong ordering between store operations and a second setting indicating weak ordering between store operations. Store operations accessing the memory subsystem are associated with either the first setting or the second setting. The data processing system also includes logic that, based upon settings of the mode field, inserts a synchronizing operation between a store operation associated with the first setting and a store operation associated with the second setting, such that all store operations preceding the synchronizing operation complete before store operations subsequent to the synchronizing operation.