In recent literature relating to drag reduction by polymeric additives, it has been purported that grafting side chains is a way of enhancing their shear stability. A careful analysis of the experimental reports shows that grafting in fact reduces the shear stability of long-chain polymers. A simple mechanistic analysis of the fracture of an ideal grafted chain molecule has been performed to support this finding. Some guidelines for the design of stable and effective drag reducing macromolecules are proposed.