Growing interest in ambitious multiple-issue machines and heavily-pipelined machines requires a careful examination of how much instruction-level parallelism exists in typical programs. Such an examination is complicated by the wide variety of hardware and software techniques for increasing the parallelism that can be exploited, including branch prediction, register renaming, and alias analysis. By performing simulations based on instruction maces, we can model techniques at the limits of feasibility and even beyond. Our study shows a striking difference between assuming that the techniques we use are perfect and merely assuming that they are impossibly good. Even with impossibly good techniques, average parallelism rarely exceeds 7, with 5 more common.