Any misspecification of the disturbance error process in a linear regression may lead to an inefficient estimator. Although spectral methods proposed by Hannan will always be asymptotically efficient, they are frequently used because they are computationally demanding and very large samples are presumably required. This paper presents Monte Carlo evidence from a variety of typical econometric situations which indicates that the estimators perform quite well for moderate-sized samples (100) when the error process is highly dependent, and even for small samples when the error process is simple. The results are used to estimate a second order term in the asymptotic expansion for the variance.