  In this paper we investigate the implications of having a varying second
slow-roll index on the canonical scalar field inflationary dynamics. We shall
be interested in cases that the second slow-roll can take small values and
correspondingly large values, for limiting cases of the function that
quantifies the variation of the second slow-roll index. As we demonstrate, this
can naturally introduce a smooth transition between slow-roll and constant-roll
eras. We discuss the theoretical implications of the mechanism we introduce and
we use various illustrative examples in order to better understand the new
features that the varying second slow-roll index introduces. In the examples we
will present, the second slow-roll index has exponential dependence on the
scalar field, and in one of these cases, the slow-roll era corresponds to a
type of $\alpha$-attractor inflation. Finally, we briefly discuss how the
combination of slow-roll and constant-roll may lead to non-Gaussianities in the
primordial perturbations.
