The major emphasis of this paper is on the definition of complete strategies in tableaux calculi for propositional modal logics. The strategies use a non exhaustive backtracking mechanism, a selective periodicity test and a uniform or a non uniform priority on the order of application of the tableaux rules. The propositional modal logics treated herein are those having a tableaux calculus with finite sets of formulas possibly occurring in the tableaux. Experimental results with the ATINF modal prover are presented.