Recently, Diebold (1986) and Wooldridge (1991) have suggested procedures for ensuring that well known tests for serial independence have asymptotically reliable sizes in the presence of conditional heteroscedasticity. This paper uses a Monte Carlo experiment to compare the sizes and powers of several versions of these robust tests with their "non-robust" forms and with standard exact tests. The general conclusion is that both robust procedures lack power and are dominated by well specified exact tests. This conclusion is not altered when the assumption of normally distributed innovations is relaxed.