  We give sufficient conditions for a group of homeomorphisms of a Peano
continuum X without cut-points to be a convergence group. The condition is that
there is a collection of convergence subgroups whose limit sets `cut up' X in
the correct fashion. This is closely related to the result in [E Swenson, Axial
pairs and convergence groups on S^1, Topology 39 (2000) 229-237].
