  We study various properties of a Proca field coupled to gravity through
minimal and quadrupole interactions, described by a two-parameter family of
Lagrangians. St\"uckelberg decomposition of the effective theory spells out its
model-dependent ultraviolet cutoff, parametrically larger than the Proca mass.
We present pp-wave solutions that the model admits, consider linear
fluctuations on such backgrounds, and thereby constrain the parameter space of
the theory by requiring null-energy condition and the absence of negative time
delays in high-energy scattering. We briefly discuss the positivity
constraints$-$derived from unitarity and analyticity of scattering
amplitudes$-$that become ineffective in this regard.
