Stabilization by over-penalization is a well-known phenomenon for specialists of model selection procedures. Indeed, it has been remarked for a long time that adding a small amount to classical penalized criteria such as AIC lead in good cases to an improvement of prediction performances, especially for moderate and small sample sizes. In particular, overfitting tends to be avoided. We propose here the first principled and general over penalization strategy and apply it to AIC. Very good results are observed in simulations.