The classical KAM methods, strongly supported on the use of canonical trans- formations in the action-angle context, are not effcient to be applied to a wide range of systems in which the Hamiltonian is known (for instance) written in Cartesian coordinates. In this communication we present some ideas to deal with KAM theory using "parameterizations" instead of "transformations" and "graphs", which we think is an effcient way to work with a more general class of Hamiltonian systems than the classical methods (in particular, for systems motivated by real world problems). With the present approach, we can extend several well-known results of KAM theory to these systems, even when the classical statements are diffcult to be applied.