In this talk I will introduce a new class of robust estimators (that I will call REWLS) for the linear regression model. They are weighted least squares estimators, with weights adaptively computed from the empirical distribution of the residuals of some initial robust estimator. It is shown that the breakdown point of the REWLS are not smaller than the breakdown point of the initial estimator, so that they can attain the maximum 1/2 breakdown point. For the particular case of the least median of squares (LMS) as the initial estimator and hard rejection weights, it is shown that the maximum bias of the REWLS for pointmass contaminations is practically equal to those of the LMS. Moreover - and this is the original contribution of this work - it is shown that the REWLS are asymptotically equivalent to the least squares estimator under the model and hence they attain the maximum asymptotic efficiency for the normal error model. To summarize, the proposed estimators attain the maximum asymptotic efficiency under the model with no damage to the robustness properties of the initial estimator. If time allows, I will also discuss the extension of this method to the Logistic Regression Model. Here a weighted maximum likelihood estimator is computed, with weights depending on the signed deviances of the observations with respect to an initial robust estimator. As in the linear regression model, this one-step estimator is asymptotically equivalent to the MLE under the model and hence fully efficient.