  Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact
special groups in terms of quasiconvex hierarchies played an essential role in
Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we
construct a new virtual quasiconvex hierarchy for relatively hyperbolic
virtually compact special groups. We use this hierarchy to prove a
generalization of Wise's Malnormal Special Quotient Theorem for relatively
hyperbolic virtually compact special groups with arbitrary peripheral
subgroups.
