This paper is concerned with testing for first-order autoregressive disturbances in the linear regression model and recommends an alternative test to the Durbin-Watson test. The new test is most powerful invariant in a given neighbourhood of the alternative hypothesis parameter space. An empirical power comparison indicates that the test is generally more powerful than the Durbin-Watson test. The comparison also suggests that for many economic applications, the difference in power will be small, although circumstances do exist in which the power advantage of the new test is very real. Selected bounds for the test's significance points are tabulated.