  The Pruning Front Conjecture is proved for an open set of H\'enon parameters
far from unimodal. More specifically, for an open subset of H\'enon parameter
space, consisting of two connected components one of which intersects the
area-preserving locus, it is shown that the associated H\'enon maps are
prunings of the horseshoe. In particular, their dynamics is a subshift of the
two-sided two-shift.
