  We classify all closed non-orientable P2-irreducible 3-manifolds having
complexity up to 6 and we describe some having complexity 7. We show in
particular that there is no such manifold with complexity less than 6, and that
those having complexity 6 are precisely the 4 flat non-orientable ones and the
filling of the Gieseking manifold, which is of type Sol. The manifolds having
complexity 7 we describe are Seifert manifolds of type H2 x S1 and a manifold
of type Sol.
