Metric perturbations typically strengthen field resonances during preheatin
g. in contrast we present a model in which the super-Hubble field resonance
s are completely suppressed when metric perturbations are included. The mod
el is the nonminimal Fakir-Unruh scenario which is exactly solvable in the
long-wavelength limit when metric perturbations are included, but exhibits
exponential growth of super-Hubble modes in their absence. This gravitation
ally enhanced integrability is exceptional, both for its rarity and for the
power with which it illustrates the importance of including metric perturb
ations in consistent studies of preheating. We conjecture a no-go result-th
ere exists no single-field model with growth of cosmologically relevant met
ric perturbations during preheating.