  Subsurface projection has become indispensable in studying the geometry of
the mapping class group and the curve complex of a surface. When the subsurface
is an annulus, this projection is sometimes called relative twisting. We give
two alternate versions of relative twisting for the outer automorphism group of
a free group. We use this to describe sufficient conditions for when a folding
path enters the thin part of Culler-Vogtmann's Outer space. As an application
of our condition, we produce a sequence of fully irreducible outer
automorphisms whose axes in Outer space travel through graphs with arbitrarily
short cycles; we also describe the asymptotic behavior of their translation
lengths.
