The convenience of using Greenberger-Horne-Zeilinger (GHZ) stales for disproving a recently proposed “hardest-to-beat” type of hidden variables theory is analyzed. The experimental conditions for observing a discrepancy from quantum mechanical predictions are obtained, for a GHZ state with an arbitrary number q of particles. It is shown that an Orsay-like experiment is preferable, even for highly idealized conditions and even if the difficulty of preparation of a GHZ state with a large number of particles is not taken into account. The (...) situation may be different for the case q=4 if a proposed theorem is demonstrated true. (shrink)