Recent advances in the theoritical analysis of optimality in model selection via penalization procedures, and more precisely concerning the validity of the Slope Heurisitcs …rst formulated by Birgé and Massart [3] and then extended by Arlot and Massart [1], have led to investigate the consistency in sup-norm of M- estimators in order to derive controls of the excess risk and of the empirical excess risk of an M-estimator, that are optimal at the …rst order (see [13], [14] and [12]). Indeed, such controls are one of the keystones to justify the Slope Heuristics, as claimed in [1]. In [13] (and also in [14]), the author has been able to show the consistency of least-squares estimators in an heteroscedastic with random design regression setting, on suitable linear models of histograms and piecewise polynomials . We investigate in the present paper a systematical approach of convergence in sup-norm for least-squares regression on …nite dimensional linear models. We give general constraints on the structure of these models that are su¢ cient to derive the consistency of the considered estimators, and these constraints appear to be slightly more restrictive than the classical assumption of localized basis. Nevertheless, our approach allows to consider for example some models of compactly supported wavelets, such as Haar expansions.