  We prove that if $\phi,\psi\in Out(F_N)$ are hyperbolic iwips (irreducible
with irreducible powers) such that $<\phi,\psi>\le Out(F_N)$ is not virtually
cyclic then some high powers of $\phi$ and $\psi$ generate a free subgroup of
rank two, all of whose nontrivial elements are again hyperbolic iwips. Being a
hyperbolic iwip element of $Out(F_N)$ is strongly analogous to being a
pseudo-Anosov element of a mapping class group, so the above result provides
analogs of "purely pseudo-Anosov" free subgroups of $Out(F_N)$.
