  We show that if $\Omega\subset\mathbb R^3$ is a two-sided NTA domain with
AD-regular boundary such that the logarithm of the Poisson kernel belongs to
$\textrm{VMO}(\sigma)$, where $\sigma$ is the surface measure of $\Omega$, then
the outer unit normal to $\partial\Omega$ belongs to $\textrm{VMO}(\sigma)$
too. The analogous result fails for dimensions larger than $3$. This answers a
question posed by Kenig and Toro and also by Bortz and Hofmann.
