  Let $\pi_1(C)$ be the fundamental group of a smooth irreducible affine curve
$C$ over an algebraically closed field of positive characteristic. It is shown
that given an embedding problem for $\pi_1(C)$ there exist an open index $p$
normal subgroup of $\pi_1(C)$ so that the embedding problem restricted to this
group has a solution. In particular, $\pi_1(C)$ is "almost $\omega$-free".
