Controlling the impact of drops onto solid surfaces is important for a wide variey of coating and deposition processes--for example, the treatment of plants with herbicides and pesticides requires precise targeting in order to meet stringent toxicological regulations. However, the outer wax-like layer of the leaves is a non-wetting substrate that causes sprayed droplets to rebound; often less than 50% of the initial spray is retained by the plant. Although the impact and subsequent retraction of non-wetting aqueous drops on a hydrophobic surface have been the subjects of extensive experimental and theoretical work, non-newtonian rheological effects have not been considered in any detail. Here we report that, by adding very small amounts of a flexible polymer to the aqueous phase, we can inhibit droplet rebound on a hydrophobic surface and markedly improve deposition without significantly altering the shear viscosity of the solutions. Our results can be understood by taking into account the non-newtonian elongational viscosity, which provides a large resistance to drop retraction after impact, thereby suppressing droplet rebound.