  In this paper, we apply reconstruction techniques to recover the potential
parameters for a particular class of single-field models, the
$\alpha$-attractor (supergravity) models of inflation. This also allows to
derive the inflaton vacuum expectation value at horizon crossing. We show how
to use this value as one of the input variables to constrain the
postaccelerated inflationary phase. We assume that the tensor-to-scalar ratio
$r$ is of the order of $10^{-3}$ , a level reachable by the expected
sensitivity of the next-generation CMB experiments.
