  We analyze the class of nonlocal realistic theories that was originally
considered by Leggett [Found. Phys. 33, 1469 (2003)] and tested by us in a
recent experiment [Nature (London) 446, 871 (2007)]. We derive an
incompatibility theorem that works for finite numbers of polarizer settings and
that does not require the previously assumed rotational symmetry of the
two-particle correlation functions. The experimentally measured case involves
seven different measurement settings. Using polarization-entangled photon
pairs, we exclude this broader class of nonlocal realistic models by
experimentally violating a new Leggett-type inequality by 80 standard
deviations.
