  We discuss the issue of perturbativity in single-field inflationary models
with a phase of ultra slow-roll (USR) tailor suited to generate an order-one
abundance of primordial black holes (PBHs). More in detail, we impose the
condition that loop corrections made up of short-wavelength modes enhanced by
the USR dynamics do not alter the tree-level power spectrum of curvature
perturbations. In our analysis, the USR phase is preceded and followed by two
stages of ordinary slow-roll (SR), and we model the resulting SR/USR/SR
dynamics using both instantaneous and smooth transitions. Focusing on scales
relevant for CMB observations, we find that it is not possible, with these
arguments, to rule out the scenario of PBH formation via USR, not even in the
limit of instantaneous transition. However, we also find that loop corrections
of short modes on the power spectrum of long modes, even though not large
enough to violate perturbativity requirements, remain appreciable and, most
importantly, are not tamed in realistic realisations of smooth SR/USR/SR
transitions. This makes perturbativity a powerful theoretical tool to constrain
USR dynamics. We extend the analysis at any scale beyond those relevant for CMB
observations. We find that loop corrections of short modes remain within the
few percent if compared to the tree-level power spectrum. However, we also find
one notable exception of phenomenological relevance: we show that the so-called
dip in the power spectrum of curvature perturbation is an artifact of the
tree-level computation.
