The shape and slip of freely drifting, two-dimensional, flexible weighted drogues tethered to a surface buoy in a specified upper-ocean velocity profile are examined numerically. A simple analytic solution for a drogue in a linear shear flow, in the limit of small deviations from a straight vertical configuration, is used to identify the parameters of the problem and to predict the functional dependence of the slip and shape of the drogue on those parameters. The numerical computations, using a finite elements static equilibrium model, confirm the functional dependence predicted by the analytic solution and estimate the parametric dependences. However, a linear shear is not the “worst case” shear one needs to design for. In optimizing a drogue for linear shear, one can make use of the symmetry of the velocity profile to minimize the slip. The design problem arises from not knowing a priori the shear for which one is designing (especially since a drogue eventually moves far from its deployment site) and from asymmetric shear (i.e., the “worst case” shear is one with a bias). The final computations examine three different drogue configurations in a series of profiles that model the diurnal cycle of the mixed layer (a diurnal jet) overlying a linear shear. The best design is found to be one that maximizes the drogue over the depth interval of interest, while minimizing the drag area of the tether. The drogue length needs to be larger than the depth interval of interest to account for the rise and tilt of the drogue in shear flow, but not so large that it averages too far outside the interval. For the practical cases considered, a drogue length that was twice the averaging interval gave the best results.