The criterion of second-order efficiency is used to distinguish among estimators, which have the same asymptotic variance, of the mean of a stationary autoregressive process. The best linear unbiased estimator is typically unknown, since it depends on the parameters of the process. It is demonstrated by second-order efficiency that the sample mean performs poorly under certain conditions, whereas some weighted averages maintain a more consistent performance as the parameters of the underlying process are allowed to vary. Numerical examples are shown for second-and third-order autoregressive processes.