  The experimental violation of Bell inequality establishes necessary but not
sufficient conditions that any theory must obey. Namely, a theory compatible
with the experimental observations can satisfy at most two of the three
hypotheses at the basis of Bell's theorem: free will, no-signaling, and
outcome-Independence. Quantum mechanics satisfies the first two hypotheses but
not the latter. Experiments not only violate Bell inequality, but show an
excellent agreement with quantum mechanics. This fact restricts further the
class of admissible theories. In this work, the author determines the form of
the hidden-variable models that reproduce the quantum mechanical predictions
for a spin singlet while satisfying both the hypotheses of free will and
no-signaling. Two classes of hidden-variable models are given as an example,
and a general recipe to build infinitely many possible models is provided.
