The input-output inversion of a system under the effect of input delays typically relies on the ability to predict the future of the system's state. Indeed, if the latter is known ahead of time, one can cope with the input delay by using a prediction of the state instead of the state itself. Such methods are efficient when the plant is stable but become numerically unstable otherwise. We present a new method to compensate input delays; our approach relies on imposing a desired error dynamics which is designed to be linear and asymptotically stable at the origin. Then, the state prediction is computed from the state reference trajectory and the predicted error dynamics. In this technical note, we concentrate on the case study of systems in strict feedback form and present a simple backstepping procedure.