A powered surgical handpiece, said handpiece including: a housing; an electric motor disposed in the housing, the motor including plural windings and a rotor having a longitudinal axis and an even number of magnets, the rotor being disposed within the windings; an output drive shaft connected to the motor rotor to be rotated by the motor rotor, the output drive shaft having an elongated bore dimensioned to receive the shaft of a cutting accessory; and a coupling assembly (84, 146, 152, 154) with at least one locking element that extends into the bore of the output drive shaft, the at least one locking element releasably holding the cutting accessory shaft to the output drive shaft so that the cutting accessory shaft rotates in unison with the output drive shaft; wherein the rotor is formed with an axially extending bore and the magnets are disposed in the rotor bore, wherein each of said magnets has: an outer surface located adjacent the bore-defining inner surface of said rotor; characterized in that: each of said magnets has two side surfaces that extend away from the outer surface and towards the longitudinal axis of said motor rotor so as to define a corner where the two sides of the magnet meet, the magnets being arranged in the rotor bore so that the corners of the magnets abut; and the magnets are arranged so that a first pole of a said magnet is located at the outer surface of the magnet and an opposed second pole is located at the corner of the magnet; and said magnets are disposed in the rotor bore so that arcuately adjacent magnets have corners with opposed magnetic polarities. a housing; an electric motor disposed in the housing, the motor including plural windings and a rotor having a longitudinal axis and an even number of magnets, the rotor being disposed within the windings; an output drive shaft connected to the motor rotor to be rotated by the motor rotor, the output drive shaft having an elongated bore dimensioned to receive the shaft of a cutting accessory; and a coupling assembly (84, 146, 152, 154) with at least one locking element that extends into the bore of the output drive shaft, the at least one locking element releasably holding the cutting accessory shaft to the output drive shaft so that the cutting accessory shaft rotates in unison with the output drive shaft; wherein the rotor is formed with an axially extending bore and the magnets are disposed in the rotor bore, wherein each of said magnets has: an outer surface located adjacent the bore-defining inner surface of said rotor; characterized in that: each of said magnets has two side surfaces that extend away from the outer surface and towards the longitudinal axis of said motor rotor so as to define a corner where the two sides of the magnet meet, the magnets being arranged in the rotor bore so that the corners of the magnets abut; and the magnets are arranged so that a first pole of a said magnet is located at the outer surface of the magnet and an opposed second pole is located at the corner of the magnet; and each of said magnets has two side surfaces that extend away from the outer surface and towards the longitudinal axis of said motor rotor so as to define a corner where the two sides of the magnet meet, the magnets being arranged in the rotor bore so that the corners of the magnets abut; and the magnets are arranged so that a first pole of a said magnet is located at the outer surface of the magnet and an opposed second pole is located at the corner of the magnet; and said magnets are disposed in the rotor bore so that arcuately adjacent magnets have corners with opposed magnetic polarities.