The notion of k-tameness of a pseudovariety was introduced by Almeida and Steinberg and is a strong property which implies decidability of pseudovarieties. In this paper we prove that the pseudovariety LSl, of local semilattices, is k-tame.This work was supported, in part, by FCT through the Centro de Matemática da Universidade do Minho, and by the FCT and POCTI approved project POCTI/32817/MAT/2000 which is comparticipated by the European Community Fund FEDER