  The paper presents a cut-elimination procedure for intuitionistic
propositional logic in which cut is eliminated directly, without introducing
the multiple-cut rule mix, and in which pushing cut above contraction is one of
the reduction steps. The presentation of this procedure is preceded by an
analysis of Gentzen's mix-elimination procedure, made in the perspective of
permuting cut with contraction. It is also shown that in the absence of
implication, pushing cut above contraction doesn't pose problems for directly
eliminating cut.
