Although mutation analysis is considered the best way to evaluate the effectiveness of a test suite, hefty computa- tional cost often limits its use. To address this problem, var- ious mutation reduction strategies have been proposed, all seeking to reduce the number of mutants while maintaining the representativeness of an exhaustive mutation analysis. While research has focused on the reduction achieved, the effectiveness of these strategies in selecting representative mutants, and the limits in doing so have not been investi- gated, either theoretically or empirically. We investigate the practical limits to the effectiveness of mutation reduction strategies, and provide a simple theoret- ical framework for thinking about the absolute limits. Our results show that the limit in improvement of effectiveness over random sampling for real-world open source programs is a mean of only 13.078%. Interestingly, there is no limit to the improvement that can be made by addition of new mutation operators. Given that this is the maximum that can be achieved with perfect advance knowledge of mutation kills, what can be practically achieved may be much worse. We conclude that more effort should be focused on enhancing mutations than removing operators in the name of selective mutation for questionable benefit.