A derivation of the BRST operator for non-critical W-strings:Dedicated to Professor F. Cerulus on the occasion of his 65th Birthday

We derive the recently proposed BRST charge for non-critical W strings from a lagrangian approach. The basic observation is that, despite appearances, the combination of two classical "matter" and "Toda" w3 systems leads to a closed modified gauge algebra, which is of the so-called soft type. Based on these observations, a novel way to construct critical w3 strings is given.