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The form of the inflationary potential is severely restricted if one requiresthat it be natural in the technical sense, i.e. terms of unrelated origin arenot required to be correlated. We determine the constraints on observables thatare implied in such natural inflationary models, in particular on $r$, theratio of tensor to scalar perturbations. We find that the naturalnessconstraint does not require $r$ to be lare enough to be detectable by theforthcoming searches for B-mode polarisation in CMB maps. We show also that thevalue of $r$ is a sensitive discriminator between inflationary models.

Fine tuning and the ratio of tensor to scalar density fluctuations from cosmological inflation