  We calculate the transverse double-spin asymmetry for the production of
dimuons in pp collisions as function of the dimuon rapidity and mass to
next-to-leading accuracy in the strong coupling. Predictions for BNL-RHIC and
HERA-N are made by assuming a saturation of Soffer's inequality at a low
hadronic input scale. It seems unlikely that transversity can be measured in
dimuon production at RHIC.
