  For quadratic polynomial $f: \mathbb{C}\to \mathbb{C}$ with connected Julia
set, the Yoccoz inequality states the multiplier $\lambda$ for a fixed point of
$f$ with combinatorial rotation number $p/q$ satisfies $|\log\lambda-2\pi i
p/q| = \mathcal{O}(1/q).$ We improve this bound to $\mathcal{O}(1/q^2)$ when
$p=1$.
