The performance effect of permitting different memory operations to be re-ordered is examined. The available parallelism is computed using a machine code simulator. A range of possible restrictions on the re-ordering of memory operations is considered: from the purely sequential case where no re-ordering is permitted; to the completely permissive one where memory operations may occur in any order so that the parallelism is restricted only by data dependencies. A general conclusion is drawn that to reliably obtain parallelism beyond 10 instructions per clock will require an ability to re-order all memory instructions. A brief description of a feasible architecture capable of this is given.