  Crooked planes were defined by Drumm to bound fundamental polyhedra in
Minkowski space for Margulis spacetimes. They were extended by Frances to
closed polyhedral surfaces in the conformal compactification of Minkowski space
(Einstein space) which we call crooked surfaces. The conformal model of anti-de
Sitter space is the interior of the quotient of Einstein space by an involution
fixing an Einstein plane. The purpose of this note is to show that the crooked
planes defined in anti-de Sitter space recently by Danciger-Gu\'eritaud-Kassel
lift to restrictions of crooked surfaces in Einstein space which are adapted
under the involution of Einstein space defining anti-de Sitter space.
