A combination includes a dental handpiece and a prophy angle. The dental handpiece includes a nosecone threadably connected to the dental handpiece. The prophy angle includes a proximal body that matingly attaches to the nosecone. A plurality of elongated torque members are formed on each of the prophy angle proximal body and the nosecone. Each of the torque members is a male torque member or a female torque member and each male torque member formed on one of the prophy angle proximal body and the nosecone matingly couples with a female torque member formed on the other of the nosecone and the prophy angle proximal body. The prophy angle, including the plurality of elongated torque members formed on the prophy angle, is formed to also be attachable to a known standard doriot-style nosecone. Other specific features of the handpiece and prophy angle are also disclosed.