The curvaton and inhomogeneous reheating scenarios for the generation of the cosmological curvature perturbation on large scales represent an alternative to the standard slow-roll scenario. The basic assumption of these mechanisms is that the initial curvature perturbation due to the inflaton field is negligible. This is usually attained by lowering the energy scale of inflation, thereby concluding that the amount of gravitational waves produced during inflation is highly suppressed. We show that the curvaton and inhomogeneous reheating scenarios are compatible with a level of gravity-wave fluctuations which may well be observed in future satellite experiments.