  The inclusion of a flat metric tensor in gravitation permits the formulation
of a gravitational stress-energy tensor and the formal derivation of general
relativity from a linear theory in flat spacetime. Building on the works of
Kraichnan and Deser, we present such a derivation using universal coupling and
gauge invariance.
  Next we slightly weaken the assumptions of universal coupling and gauge
invariance, obtaining a larger ``slightly bimetric'' class of theories, in
which the Euler-Lagrange equations depend only on a curved metric, matter
fields, and the determinant of the flat metric. The theories are equivalent to
generally covariant theories with an arbitrary cosmological constant and an
arbitrarily coupled scalar field, which can serve as an inflaton or dark
matter.
  The question of the consistency of the null cone structures of the two
metrics is addressed. A difficulty for Logunov's massive gravitation on this
front is noted.
