Summary: On an explicit example of the Siegel superparticle we study an alternative to the harmonic superspace approach. The latter seems to be the only method for quantizing infinitely reducible first class constraints currently available. In an appropriately extended phase space, the infinite ghost tower is effectively canceled by that coming from the sector of auxiliary variables. After a proper BRST treatment the theory proves to be of rank two which correlates well with the results obtained earlier within the framework of the harmonic superspace approach. The advantage of the novel technique, however, is the existence of an explicit Lagrangian formulation and the standard spin–statistics relations which hold for all the variables involved.