  The existence of several nilpotent Noether charges in the decoupled
formulation of two-dimensional gauge theories does not imply that all of these
are required to annihilate the physical states. We elucidate this matter in the
context of simple quantum mechanical and field theoretical models, where the
structure of the Hilbert space is known. We provide a systematic procedure for
deciding which of the BRST conditions is to be imposed on the physical states
in order to ensure the equivalence of the decoupled formulation to the
original, coupled one.
