  The detection of primordial gravitational waves, or tensor perturbations,
would be regarded as compelling evidence for inflation. The canonical measure
of this is the ratio of tensor to scalar perturbations, r. For single-field
slow-roll models of inflation with small field excursions, the Lyth bound
dictates that if the evolution of the slow-roll parameter epsilon is monotonic,
the tensor-to-scalar ratio must be below observationally detectable levels. We
describe how non-monotonic evolution of epsilon can evade the Lyth bound and
generate observationally large r, even with small field excursions. This has
consequences for the scalar power spectrum as it necessarily predicts an
enhancement in the spectrum at very small scales and significant
scale-dependent running at CMB scales. This effect has not been appropriately
accounted for in previous analyses. We describe a mechanism that will
generically produce the required behaviour in epsilon and give an example of
this mechanism arising in a well-motivated small-field model. This model can
produce r\geq0.05 while satisfying all current observational constraints.
