  A simplicial complex is called negatively curved if all its simplices are
isometric to simplices in hyperbolic space, and it satisfies Gromov's Link
Condition. We prove that, subject to certain conditions, a compact graph of
spaces whose vertex spaces are negatively curved 2-complexes, and whose edge
spaces are points or circles, is negatively curved. As a consequence, we deduce
that certain groups are CAT(-1). These include hyperbolic limit groups, and
hyperbolic groups whose JSJ components are fundamental groups of negatively
curved 2-complexes---for example, finite graphs of free groups with cyclic edge
groups.
