  Successful inflationary models should (i) describe the data well; (ii) arise
generically from sensible UV completions; (iii) be insensitive to detailed
fine-tunings of parameters and (iv) make interesting new predictions. We argue
that a class of models with these properties is characterized by relatively
simple potentials with a constant term and negative exponentials. We here
continue earlier work exploring UV completions for these models, including the
key (though often ignored) issue of modulus stabilisation, to assess the
robustness of their predictions. We show that string models where the inflaton
is a fibration modulus seem to be robust due to an effective rescaling
symmetry, and fairly generic since most known Calabi-Yau manifolds are
fibrations. This class of models is characterized by a generic relation between
the tensor-to-scalar ratio $r$ and the spectral index $n_s$ of the form $r
\propto (n_s -1)^2$ where the proportionality constant depends on the nature of
the effects used to develop the inflationary potential and the topology of the
internal space. In particular we find that the largest values of the
tensor-to-scalar ratio that can be obtained by generalizing the original set-up
are of order $r \lesssim 0.01$. We contrast this general picture with specific
popular models, such as the Starobinsky scenario and $\alpha$-attractors.
Finally, we argue the self consistency of large-field inflationary models can
strongly constrain non-supersymmetric inflationary mechanisms.
