We consider two families of fuzzy propositional logics obtained by extendirig MTL and IMTL with the n-contraction axiom, for n > 2. These logics - called Cn-MTL and Cn-IMTL - range from Gödel and classical logic (when n = 2) to MTL and IMTL (when n tends to infinity), respectively. We investigate the t-norm based semantics and the proof theory for Cn-MTL and Cn-IMTL. We show standard cornpleteness and suitable analytic hypersequent calculi for theni.