The use of the Box-Cox family of transformations is a popular approach to make data behave according to a linear regression model. The regression coefficients, as well as the parameter A defining the transformation, are generally estimated by maximum likelihood, assuming homoscedastic normal errors. These estimates are nonrobust; in addition, consistency to the true parameters holds only if the assumptions of normality and homoscedasticity are satisfied. We present here a new class of estimates, for the case of simple regression, which are robust and consistent even if the assumptions of normality and homoscedasticity do not hold.