The optimum current density distribution for stress-limited, high-field, high-power magnets can be approached by magnets built up of many thin coils, to maximize their efficiency ("tesla per watt"). By optimizing the radial thickness and height of each subcoil, magnets consisting of only 8 Bitter coils can closely approximate the optimum. For instance, with 24 MW such a magnet of inner and outer radii of 28 mm and 420 mm, respectively, could generate over 30 T. We therefore propose a new method of magnet construction, the Poly-Bitter Magnet.