  A parameter-free calculation for J/Psi suppression in pA collisions, based on
the dipole description, is confronted with the new data from the PHENIX
experiment. Achieving good agreement, we employed this model predicting the
contribution of initial state interactions (ISI) to J/Psi suppression in AA
collisions. Such a transition from pA to AA is not straightforward, since
involves specific effects of double color filtering and boosting of the
saturation scale. Relying on this refined ISI contribution, we updated the
previous analysis of RHIC data on J/Psi production in Cu-Cu and Au-Au
collisions at \sqrt{s}=200 GeV, and determined the transport coefficient of the
created dense medium at q_0=0.6 GeV^2/fm. Nuclear effects for J/Psi production
at the LHC are predicted using the transport coefficient q_0=0.8 GeV^2/fm,
extracted from data on suppression of high-p_T hadrons in central lead-lead
collisions at \sqrt{s}=2.76 TeV. Our analysis covers only direct J/Psi
production, while data may also include the feed-down from decay of heavier
states and B-mesons.
