An abrading tool includes a base member having a support portion defining a first level, and a plurality of integral raised islands extending upwardly above the first level. The base member may be formed of metal or a non-conductive material. The islands are spaced apart from one another. Each island includes a respective tip portion. The distance between adjacent islands may be greater than the width of a single island. An abrasive composite material, including a carrier material and particles of an abrasive material, is affixed to the tip portions of at least some of the islands. The abrasive material may be applied by electroplating, electroless plating, brazing or another method. The abrasive material is applied only to the tip portion of the islands, such that the first level of the support portion is substantially free of the abrasive material. Methods of making the abrading tool are also described.