This paper examines the efficiency problem involved in experimental tests of so-called “local” hidden variables. It separates the phenomenological locality at issue in the Bell case from Einstein's different conception of locality, and shows how phenomenological locality also differs from the factorizability needed to derive the Bell inequalities in the stochastic case. It then pursues the question of whether factorizable, local models (or, equivalently, deterministic ones) exist for the experiments designed to test the Bell inequalities, thus rendering the experimental argument (...) against them incomplete. This leads to an investigation of the so-called “prism models” and to new inequalities for a significant class of such models, inequalities that are testable even at the low efficiencies of the photon correlation experiments. (shrink)