We investigate power transformations in nonlinear regression problems when there is a physical model for the response but little understanding of the underlying error structure. In such circumstances, and unlike the ordinary power transformation model, both the response and the model must be transformed simultaneously and in the same way. We show by an asymptotic theory and a small Monte Carlo study that for estimating the model parameters there is little cost for not knowing the correct transform a priori; this is in dramatic contrast to the results for the usual case where only the response is transformed. Possible applications of the theory are illustrated by examples.