This paper presents a statistical decision procedure for lexical ambiguity resolution. The algorithm exploits both local syntactic patterns and more distant collocational evidence, generating an efficient, effective, and highly perspicuous recipe for resolving a given ambiguity. By identifying and utilizing only the single best disambiguating evidence in a target context, the algorithm avoids the problematic complex modeling of statistical dependencies. Although directly applicable to a wide class of ambiguities, the algorithm is described and evaluated in a realistic case study, the problem of restoring missing accents in Spanish and French text. Current accuracy exceeds 99% on the full task, and typically is over 90% for even the most difficult ambiguities.