  We introduce a new class of automorphisms $\varphi$ of the non-abelian free
group $F_N$ of finite rank $N \geq 2$ which contains all iwips (= fully
irreducible automorphisms), but also any automorphism induced by a
pseudo-Anosov homeomorphism of a surface with arbitrary many boundary
components. More generally, there may be subgroups of $F_N$ of rank $\geq 2$ on
which $\varphi$ restricts to the identity.
  We prove some basic facts about such {\em tree-irreducible} automorphisms,
and show that, together with Dehn twist automorphisms, they are the natural
basic building blocks from which any automorphism of $\FN$ can be constructed
in a train track set-up. We then show:
  {\bf Theorem:} {\it Every tree-irreducible automorphism of $F_N$ has induced
North-South dynamics on the Thurston compactification $\bar{\rm CV}_N$ of Outer
space.}
  Finally, we define a "blow-up" construction on the vertices of a train track
map, which, starting from iwips, produces tree-irreducible automorphisms which
in general are not iwip.
