A modified Newton algorithm for the estimation of parameters in models containing the Box-Cox transformation is presented. It is shown that the usual maximum likelihood estimator for theklinear parameters and thempower transformation parameters may be specified as anm-parameter nonlinear least squares estimator. Several models containing Box-Cox transformations are estimated and the speed and efficiency of the modified algorithm compared with three other gradient estimation techniques. The modified Newton algorithm obtains the same parameter estimates, but two to four times faster.