We present a Leggett-type model that reproduces quantum correlations for the Bell states. It cannot be falsified through known tests based on Bell-type, Leggett-type, or so-called chained Bell inequalities. The model entails partial suppression of measurement independence (free will) to a fraction of 1/4, as quantified by a recently proposed measure that varies between 0 and 1. This is a consequence of assuming a possible nonlocal relationship between an entangler and one of two measuring stations, thereby differing from the usual nonlocal, Leggett-type models. Furthermore, the model admits arbitrary time ordering for events occurring at two spacelike separated measuring stations. The predicted correlations reproduce the quantum-mechanical ones. Thus, the model is not falsified by so-called before-before tests. © 2013 American Physical Society.