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. Transverse momentum dependent (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.