  Crooked planes are piecewise linear surfaces that were introduced by Drumm in
the early 1990s to construct fundamental domains for properly discontinuous
actions of free groups on Minkowski 3-space. In a previous paper, we introduced
analogues of these surfaces, called AdS crooked planes, in the 3-dimensional
anti-de Sitter space AdS^3; we showed that many properly discontinuous actions
of free groups on AdS^3 admit fundamental domains bounded by AdS crooked
planes. Here we study further the question of which proper actions on AdS^3
admit crooked fundamental domains, and show that some do not, in contrast to
the Minkowski setting.
