  We study the influence of unitarity corrections on the Drell-Yan transverse
momentum distribution within the color dipole approach. These unitarity
corrections are implemented through the multiple scattering Glauber-Mueller
approach, which is contrasted with a phenomenological saturation model. The
process is analyzed for the center of mass energies of the Relativistic Heavy
Ion Collider (RHIC, $\sqrt{s}=500$ GeV) and of the Large Hadron Collider (LHC,
$\sqrt{s}=14$ TeV). In addition, the results are extrapolated down to current
energies of proton-proton collisions, where non-asymptotic corrections to the
dipole approach are needed. It is also shown that in the absence of saturation,
the dipole approach can be related to the QCD Compton process.
