A drill bit for cutting hard and abrasive materials has cutting lips formed from sintered polycrystalline diamond (PCD) or polycrystalline cubic boron nitride (PCBN) contained in one or more inserts installed in a drill bit blank. The inserts are made by forming depressions in the upper surface of a matrix slab of tungsten carbide, filling the depressions with fine mesh grains of diamonds or cubic born nitride, subjecting the slab to heat and pressure sufficient to fuse the grains to one another and to the surrounding matrix walls, and then cutting the matrix slab to remove individual inserts containing an elongated vein having an exposed PCD or PCBN surface supported by at least one and preferably two or more side walls of tungsten carbide. A rectangular slot having side walls parallel to one another and equidistant from the diameter of a cylindrical drill bit blank is cut into one transverse end wall of the blank, and one or more inserts placed in the slot. The tungsten carbide walls of the inserts are then brazed to the adjacent side walls of the slot. The bit is then ground to a desired configuration, in which PCD or PCBN material forms at least part of at least one cutting lip of the finished drill bit. Preferably, flutes are formed in drill bit blank as part of the grinding operation.