  String theory models of axion monodromy inflation exhibit scalar potentials
which are quadratic for small values of the inflaton field and evolve to a more
complicated function for large field values. Oftentimes the large field
behaviour is gentler than quadratic, lowering the tensor-to-scalar ratio. This
effect, known as flattening, has been observed in the string theory context
through the properties of the DBI+CS D-brane action. We revisit such flattening
effects in type IIB flux compactifications with mobile D7-branes, with the
inflaton identified with the D7-brane position. We observe that, with a generic
choice of background fluxes, flattening effects are larger than previously
observed, allowing to fit these models within current experimental bounds. In
particular, we compute the cosmological observables in scenarios compatible
with closed-string moduli stabilisation, finding tensor-to-scalar ratios as low
as r ~ 0.04. These are models of single field inflation in which the inflaton
is much lighter than the other scalars through a mild tuning of the
compactification data.
