  We discuss in detail the relation between the gauge fixed and gauge invariant
BRST cohomology. We showed previously that in certain gauges some cohomology
classes of the gauge-fixed BRST differential do not correspond to gauge
invariant observables. We now show that in addition ``accidental'' conserved
currents may appear. These correspond one-to-one to observables that become
trivial in this gauge. We explicitly show how the gauge-fixed BRST cohomology
appears in the context of the Quantum Noether Method.
