  We propose a systematic procedure that solves the Dirac bracket commutators.
The method is based on the Gauge Unfixing formalism, a procedure that converts
second class systems into first class ones without the enlargement of the
original phase space variables. We verify that the gauge invariant variables
satisfy the Dirac bracket when we strongly impose the discarded second class
constraint. Thus, we can derive physical operators that satisfy the Dirac
commutators. In order to illustrate our procedure, three second class
constrained systems are considered. Firstly, the free particle on the two
dimensional sphere is treated. The second case considered is the noncommutative
free particle and the third is the doubly special relativity particle.
