Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $\epsilon$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $\epsilon$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.