Ping-pong and outer space

We prove that, if φ, ψ ∈ Out(F _N) are hyperbolic iwips (irreducible with irreducible powers) such that 〈φ, ψ〉 ⊆ Out(F _N) is not virtually cyclic, then some high powers of φ and ψ generate a free subgroup of rank two for which all 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 analogues of "purely pseudo-Anosov" free subgroups in Out(F _N).