  We improve on the strong uniqueness results of [GLM+17], which deal with the
following system of SDE. \begin{align*} dX_t&=Y_tdt \\
dY_t&=|X_{t}|^{\alpha}dB_t \end{align*} and $X_0=x_0,Y_0=y_0$. For
$(x_0,y_0)\ne(0,0)$, we show that short-time uniqueness holds for
$\alpha>-1/2$.
