We first present modified parameterizations for model reference adaptive control of linear plants with partial knowledge of the stable zero or pole dynamics. The modified adaptive controllers reduce the closed-loop system order by 2n(r) where n(r) is the order of the known dynamics. We then apply such parameterizations to the adaptive inverse control of plants with unknown nonsmooth nonlinearities such as a dead-zone, backlash, or hysteresis at the input or output of a linear part whose stable zero or pole dynamics are partially known. The modified designs for nonlinear plants aPchieve an order reduction 2n(r)p where p is the number of parameters of the input or output nonlinearity.