We will show that a heteroscedasticity corrected GMM estimator can improve upon the performance of the least squares estimator in certain, iid error, classical linear regression models, even though there is no heteroscedasticity to correct. Consider the classical linear regression model
Throughout, we will assume that the error sequence 
is
independent and identically distributed with common distribution function F.
Under plausible conditions on F we find an unbiased estimator,
, of 
with strictly smaller covariance matrix
than the classical Gauss-Markov estimator 
.
Our estimator, which we call the Falstaff estimator for reasons
which will become gradually apparent,
is a variant on generalized method of moments estimators which have
attracted considerable recent interest in the literature.