Synthetic tableaux method (STM) is a semantically-motivated proof and model-seeking method which, on the contrary to the Beth-like tableaux, is based on a direct reasoning. In case of finite-valued extensional propositional logics (as Classical Propositional Calculus or Lukasiewicz's L3 calculus) STM forms both effective and convincing decision procedure. An application of STM to CLuN enables one to establish, within a single tableau, characteristics of all the relevant models or countermodels of any given formula (or a set of formulas), and to localize relevant inconsistencies.