  We consider adaptive control problem in presence of nonlinear parametrization
of uncertainties in the model. It is shown that despite traditional approaches
require for domination in the control loop during adaptation, it is not often
necessary to use such energy inefficient compensators it in wide range of
applications. In particular, we show that recently introduced adaptive control
algorithms in finite form which are applicable to monotonic parameterized
systems can be extended to general smooth non-monotonic parametrization. These
schemes do not require any damping or domination in control inputs.
