In a linear regression model, when errors are autocorrelated, several asymptotically efficient estimators of parameters have been suggested in the literature. In this paper we study their small sample efficiency using Monte Carlo methods. While none of these estimators turns out to be distinctly superior to the others over the entire range of parameters, there is a definite gain in efficiency to be had from using some two-stage procedure in the presence of moderate high levels of serial correlation in the residuals and very little loss from using such methods when the true ρ is small. Where computational costs are a consideration a mixed strategy of switching to a second stage only if the estimated is higher than some critical value is suggested and is shown to perform quite well over the whole parameter range.