A series of superconducting La 2−x Sr x CuO 4 thin films, with 0.09 x 0.22, is grown over (100)SrTiO 3 substrates by means of a novel pulsed laser deposition method devised to increase the homogeneity and control of doping. We employ two separate parent oxide targets that receive ablation shots at arbitrary computer-controlled relative rates, instead of the conventional procedure that uses a single target whose doping determines the one of the film. We characterize the films both through conventional techniques (XRD, SEM, AFM and EDX) and by measuring their superconducting transition with a high-sensitivity SQUID magnetometer. The latter allows one to determine not only their average critical temperatures Tc (x) but also their dispersions due to inhomogeneities, T c (x). For Tc (x) we obtain the conventional parabolic law centered at x = 0.16, plus a Gaussian depression near x = 1/8 with a Tc -height of about 5 K and x-width about 0.03. For T c (x) we obtain, for all the dopings, values among the lowest reported up to now for La 2−x Sr x CuO 4 . The T c (x) dependence can be explained in terms of the unavoidable randomness of the positioning of the Sr ions (the so-called intrinsic chemical inhomogeneity) and a separate residual T c -inhomogeneity contribution of the order of 0.5 K, this last associated with the samples' structural inhomogeneities and films' substrate.