  On one side, so far a great part of the evidence accepted as proof of the
alleged quantum non-locality relied on inhomogeneous Bell inequalities
involving an additional assumption (no-enhancement) whose role had not been
sufficiently examined (in contrast to homogeneous inequalities, where the role
of low detection rates is well acknowledged). A first contribution of this
paper is to provide explicit examples of how a model of hidden local variables
(LHV) defying no-enhancement is able to produce a violation of an inhomogeneous
inequality, a possibility that so far was pointed out only in qualitative
terms. On the other hand, recent tests have attempted to overcome this reliance
on supplementary assumptions, but still give rise to doubt, due to:
  (i) violations are extremely low, which points to some systematical error
(the fact that alleged random errors of the detectors seem to conspire to
interfere exactly at such narrow strip around the frontier with local-realism
and not a different part of the spectrum that QM would theoretically produce
can hardly be considered just coincidence);
  (ii) the correspondence between the observations and one or another quantum
state is not clear either, as recent models cannot be really validated against
the available data (they have equal or more parameters than restrictions).
  Following (ii), it would be convenient to verify a more significant set of
quantum predictions, instead of just the few counting rates involved in a
particular Bell inequality. Finally, another type of "no-go" tests (an instance
of which we examine here) also present subtleties which call for serious
examination.
