  We estimate the Cronin effect in pA collisions at the CERN LHC and at RHIC,
using a Glauber-Eikonal model of initial state multiparton interactions. For a
correct determination of the initial parton flux, we upgrade the model cross
section, taking carefully into account all kinematical constraints of each
multi-parton interaction process. As compared with previous results, derived
with approximate kinematics, we obtain a softer spectrum of produced partons,
while improving the agreement of the model with the recent measurements of
neutral pions production in d+Au collisions at sqrt(s)=200 AGeV.
