  The depletion of gluons as the parton flux traverses a nucleus in a heavy-ion
collision can influence the production rate of heavy-quark states. Thus the
suppression of $J/\psi$ can be due to gluon depletion in the initial state in
addition to nuclear and hadronic absorption in the final state. A formalism is
developed to describe the depletion effect. It is shown that, without
constraints from other experimental facts beside the $J/\psi$ suppression data
in $pA$ and $AB$ collisions, it is not possible to determine the relative
importance of depletion vs absorption. Possible relevance to the enhanced
suppression seen in the $Pb - Pb$ data is mentioned but not studied.
