  We introduce the condition of a profinite group being semi-free, which is
more general than being free and more restrictive than being quasi-free. In
particular, every projective semi-free profinite group is free. We prove that
the usual permanence properties of free groups carry over to semi-free groups.
Using this, we conclude that if k is a separably closed field, then many field
extensions of k((x,y)) have free absolute Galois groups.
