This paper considers the problem of testing the null hypothesis of firstorder autoregressive disturbances in the linear regression model against the alternative that the disturbances follow a joint first-order, simplefourth- order autoregressive process. The class of approximate point optimal invariant tests are discussed and rules are given for choosing an appropriate member from this class of tests. The beneficial nature of these rules are illustrated by a limited empirical power comparison which shows the recommended test has good small sample power properties.