The drift of a deformable droplet of low viscosity (viscosity ratio &lgr;=0.08) in a Couette device is examined. The drift is measured both in the plane of shear (due to the rigid outer bounding walls of the Couette device) and also normal to the plane of shear (due to the upper bounding stress‐free surface). A general relationship between normal stresses induced by the deformation of a droplet in an arbitrary shear flow and the leading‐order drift normal to rigid and stress‐free plane surfaces is described theoretically. This relationship is consistent with previous theoretical predictions for droplet migration in shear flows, and is used to compare results from the drift measurement experiments with first‐order deformation theories. The measured drift velocities are in reasonable agreement with the theory of Schowalteretal. [J. Colloid Interface Sci.26, 152 (1968)].