  We evaluate the Cronin effect in pA collisions at the CERN LHC and at RHIC in
the framework of Glauber-Eikonal model of initial state multiparton
interactions. Taking carefully into account all kinematical constraints of each
multi-parton interaction process we obtain a softening of the spectrum of
produced partons, improving in this way the agreement of the model with the
recent measurements of pi0 production in d+Au collisions at sqrt{s}=200 AGeV.
