  We study double transverse spin asymmetries in the Drell-Yan process at
measured transverse momentum of the lepton pair. Contrary to what a collinear
factorization approach would suggest, a nonzero double transverse spin
asymmetry in the laboratory frame a priori does not imply nonzero transversity.
TMD effects, such as the double Sivers effect, in principle form a background.
Using the current knowledge of the relevant TMDs we estimate their contribution
in the laboratory frame for Drell-Yan and W production at RHIC and point out a
cross check asymmetry measurement to bound the TMD contributions. We also
comment on the transverse momentum integrated asymmetries that only receive
power suppressed background contributions.
