This paper investigates the limitations on designing a processor which can sustain an execution rate of greater than one instruction per cycle on highly-optimized, non-scientific applications. We have used trace-driven simulations to determine that these applications contain enough instruction independence to sustain an instruction rate of about two instructions per cycle. In a straightforward implementation, cost considerations argue strongly against decoding more than two instructions in one cycle. Given this constraint, the efficiency in instruction fetching rather than the complexity of the execution hardware limits the concurrency attainable at the instruction level.