  We embed second class constrained systems by a formalism that combines
concepts of the BFFT method and the unfixing gauge formalism. As a result, we
obtain a gauge-invariant system where the introduction of the Wess-Zumino (WZ)
field is essential. The initial phase-space variables are gauging with the
introduction of the WZ field, a procedure that resembles the St\"uckelberg
field- shifting formalism. In some cases, it is possible to eliminate the WZ
field and, therefore, obtain an invariant system written only as a function of
the original phase-space variables. We apply this formalism to important
physical models: the reduced-SU(2) Skyrme model and the two dimensional chiral
bosons field theory. In these systems, the gauge-invariant Hamiltonians are
derived in a very simple way when compared with other usual formalisms.
