For a normal sample with unknown mean, the almost universally used estimator of the variance, σ2, is “the sample variance.” This estimator is the minumum variance unbiased estimator of σ2, but it is inadmissible under square error loss. It is dominated by the maximum likelihood estimator, which is also inadmissible. We consider a class of estimators and compare these estimators under a class of loss functions which we call “log symmetric.”