  A toy model (suggested by Klauder) is analyzed from the perspective of First
Class and Second Class Dirac constrained systems. The comparison is made by
turning a First Class into a Second Class system with the introduction of
suitable auxiliary conditions. The links between Dirac's system of constraints,
the Faddeev-Popov canonical functional integral method and the Maskawa-Nakajima
procedure to reduced phase space are explicitly illustrated. The model reveals
stark contrasts and physically distinguishable results between First and Second
class routes. Physically relevant systems such as the relativistic point
particle and electrodynamics are briefly recapped. Besides its pedagogical
value, the article also advocates the route of rendering First Class into
Second Class systems prior to quantization. Second Class systems lead to
well-defined reduced phase space and physical observables; absence of
inconsistencies in the closure of quantum constraint algebra; and consistent
promotion of fundamental Dirac brackets to quantum commutators. As First Class
systems can be turned into well-defined Second Class ones, this has
implications for the soundness of "Dirac quantization" of First Class
constrained systems by simple promotion of Poisson, rather than Dirac brackets,
to commutators without proceeding through Second Class procedures.
