  This paper explores in some detail a recent proposal (the Rieffel
induction/refined algebraic quantization scheme) for the quantization of
constrained gauge systems. Below, the focus is on systems with a single
constraint and, in this context, on the uniqueness of the construction. While
in general the results depend heavily on the choices made for certain auxiliary
structures, an additional physical argument leads to a unique result for
typical cases. We also discuss the `superselection laws' that result from this
scheme and how their existence also depends on the choice of auxiliary
structures. Again, when these structures are chosen in a physically motivated
way, the resulting superselection laws are physically reasonable.
