It is possible to construct a test of the null of no fractional integration that has nontrivial asymptotic power against a sequence of alternatives specifying that the series is I(d) with d = O(T−1/2), where T is the sample size. In this paper, I show that tests for fractional integration that are based on the partial sum process of the time series have only trivial asymptotic power (i.e., equal to the size) against this sequence of local alternatives. These tests include the rescaled-range test. In this sense, despite its widespread use in empirical work, the rescaled-range test is a poor test for fractional integration.