  For systems which contain both superselection structure and constraints, we
study compatibility between constraining and superselection. Specifically, we
start with a generalisation of Doplicher-Roberts superselection theory to the
case of nontrivial centre, and a set of Dirac quantum constraints and find
conditions under which the superselection structures will survive constraining
in some form. This involves an analysis of the restriction and factorisation of
superselection structures. We develop an example for this theory, modelled on
interacting QED.
