  In this paper, the formation of primordial black holes (PBHs) is
reinvestigated using inflationary $\alpha$-attractors. Instead of using the
conventional Press-Schechter theory to compute the abundance, the optimized
peaks theory is used, which was developed in Ref.
\cite{Yoo:2018kvb,Yoo:2020dkz}. This method takes into account how curvature
perturbations play a r\^{o}le in modifying the mass of primordial black holes.
Analyzing the model proposed in \cite{Mahbub:2019uhl} it is seen that the
horizon mass of the collapsed Hubble patch is larger by $\mathcal{O}(10^2)$
compared to the usual computation. Moreover, PBHs can be formed from curvature
power spectrum, $\mathcal{P}_{\zeta}(k)$, peaked at lower values using
numerically favored threshold overdensities. As a result of the generally
larger masses predicted, the peak of the power spectrum can be placed at
$k>10^{15}\text{Mpc}^{-1}$ with which potential future constraints on the
primordial power spectrum through gravitational waves (GWs) can be evaded.
