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We note that the subpolynomial factor for the $\ell^qL^p$ small capdecoupling constants for the truncated parabola $\mathbb{P}^1=\{(t,t^2):|t|\leq1\}$ may be controlled by a suitable power of $\log R$. This is achieved byconsidering a suitable amplitude-dependent wave envelope estimate, as wasintroduced in a recent paper of Guth and Maldague to demonstrate a small capdecoupling 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 $\log R$ aswell.

Small cap decoupling for the parabola with logarithmic constant