  We show that the "practical" Bell inequalities, which use intensities as the
observed variables, commonly used in quantum optics and widely accepted in the
community, suffer from an inherent loophole, which severely limits the range of
local hidden variable theories of light, which are invalidated by their
violation. We present alternative inequalities which do not suffer from any
(theoretical) loophole. The new inequalities use redefined correlation
functions, which involve averaged products of local rates rather than
intensities. Surprisingly, the new inequalities detect entanglement in
situations in which the "practical" ones fail. Thus, we have two for the price
on one: full consistency with Bell's Theorem, and better device-independent
detection of entanglement.
