We discuss a KAM theorem for elliptic lower dimensional tori of Hamiltonian systems via parameterizations. The method is based in solving iteratively the functional equations that stand for invariance and reducibility. In contrast with classical methods, we do not assume that the system is close to integrable nor that it is written in action-angle variables. We want to highlight that the approach presents many advantages compared with methods which are built in terms of canonical transformations, e.g., it produces simpler and more constructive proofs that lead to more efficient numerical algorithms for the computations of these objects. This is a joint work with Jordi Villanueva.