  In this article we prove new results about the existence of 2-cells in disc
diagrams which are extreme in the sense that they are attached to the rest of
the diagram along a small connected portion of their boundary cycle. In
particular, we establish conditions on a 2-complex X which imply that all
minimal area disc diagrams over X with reduced boundary cycles have extreme
2-cells in this sense. The existence of extreme 2-cells in disc diagrams over
these complexes leads to new results on coherence using the perimeter-reduction
techniques we developed in an earlier article. Recall that a group is called
coherent if all of its finitely generated subgroups are finitely presented. We
illustrate this approach by showing that several classes of one-relator groups,
small cancellation groups and groups with staggered presentations are
collections of coherent groups.
