A drain-cleaning machine comprises a cable, a motor assembly, and a speed control assembly. The cable comprises a longitudinal axis. The motor assembly is configured to rotate the cable about the longitudinal axis of the cable. The motor assembly comprises a motor and a motor control device. The motor is configured to operate at an operating speed that may vary within a range of operating speeds. The motor is configured to produce a substantially constant torque while operating at varying operating speeds across the entire range of operating speeds. The motor is configured to be powered by DC power. The motor control device is configured to receive AC power from an AC power source, convert the AC power into DC power, and communicate the DC power to the motor. The speed control assembly is configured to vary the operating speed of the motor within the range of operating speeds.