When the deflection of a tethered spherical balloon from the vertical is used to measure the strength and direction of a light low-level wind, the gravity and wind drag forces on the tether may have a significant influence, producing a curvature in the tether and changing the direction of its pull on the balloon. A technique has been developed for accurately calculating the effect of these forces. The measurements required for the technique are the free lift of the balloon, the length, diameter, and weight of the tether, and either the orientation of the balloon from the ground tether point (the generally preferred method), or the orientation of the tether near the ground (appropriate in foggy conditions). Some examples are given which indicate the conditions under which the forces on the tether are important, and some measurements are set out which show that the technique gives good results.