  In this paper we give a new, less restrictive condition for removability of
singular sets, $E$, of smooth solutions to the m-Hessian equation (and also for
more general fully nonlinear elliptic equations) in $\Omega \setminus E$,
$\Omega \subset \mathbb R^n$. Besides the existence and regularity results for
these equations, the proof only makes use of the classical elliptic theory,
i.e. the classical maximum principles and a Hopf lemma.
