  We note that the subpolynomial factor for the $\ell^qL^p$ small cap
decoupling constants for the truncated parabola $\mathbb{P}^1=\{(t,t^2):|t|\leq
1\}$ may be controlled by a suitable power of $\log R$. This is achieved by
considering a suitable amplitude-dependent wave envelope estimate, as was
introduced in a recent paper of Guth and Maldague to demonstrate a small cap
decoupling for the $(2+1)$ cone; we demonstrate that the version for
$\mathbb{P}^1$ may be taken with a loss controlled by a power of $\log R$ as
well.
