New strategies of reduction for finite-valued propositional logics are introduced in the framework of the TAS1 methodology developed by the authors [1]. A new data structure, the Δ^-sets, is introduced to store information about the formula being analysed, and its usefulness is shown by developing efficient strategies to decrease the size of signed propositional formulas, viz., new criteria to detect the validity or unsatisfiability of subformulas, and a strong generalisation of the pure literal rule.