This paper discusses ways to reduce the bias of consistent estimators that are biased in finite samples. It is necessary that the bias function, which relates parameter values to bias, should be estimable by computer simulation or by some other method. If so, bias can be reduced or, in some cases that may not be unrealistic, even eliminated. In general, several evaluations of the bias function will be required to do this. Unfortunately, reducing bias may increase the variance, or even the mean squared error, of an estimator. Whether or not it does so depends on the shape of the bias functions. The techniques of the paper are illustrated by applying them to two problems: estimating the autoregressive parameter in an AR(1) model with a constant term, and estimation of a logit model.