  The BRST quantisation of the Drinfeld - Sokolov reduction is exploited to
recover all singular vectors of the Virasoro algebra Verma modules from the
corresponding $A^{(1)}_1\,$ ones. The two types of singular vectors are shown
to be identical modulo terms trivial in the $Q_{BRST}$ cohomology. The main
tool is a quantum version of the DS gauge transformation.
