  Given a group acting cellularly and cocompactly on a simply-connected
2-complex, we provide a criterion establishing that all finitely generated
subgroups have quasiconvex orbits. This work generalizes the "perimeter
method". As an application, we show that high-powered one-relator products $A
\ast B / \nclose{r^n}$ are coherent if $A$ and $B$ are coherent.
