Green and Laffont have characterized certain appealing dominant-strategy revelation mechanisms as precisely the mechanisms introduced by Groves, but they have established the characterization only for unstructured sets of public alternatives: if the set has some natural structure, their proof generally requires that pathological preferences be admissible. It is shown here that the same characterization holds on sets in R^n, even when only nice preferences are admitted; this greatly extends the usefulness of the characterization.