In this note, we point out alternative proofs of the results of the paper \citeKrstic-Sun-Kokotovic, using alternative controllers. In that paper, Krstic, Sun and Kokotovic solve various stabilization problems in presence of input unmodelled dynamics. Their solution incorporates, in the controller, a signal, called normalizing signal, which captures the effect of the unmodelled dynamics. Here, we show that this signal is not needed. This result is obtained via an appropriate change of coordinates of the unmodelled dynamics and by applying the technique of propagating the ISS property through integrators proposed in \citeJiang-Praly-Teel. The dimension of the state of our controllers is smaller than that of the corresponding controllers in \citeKrstic-Sun-Kokotovic.