A motor-drive system for retractable covering having a headrail with a horizontally disposed roller supporting a top edge of a flexible fabric material includes an electric motor mounted within a housing and interconnected to the roller to selectively rotate the roller in opposite directions while minimizing noise created from vibrations within the system. This system includes motor mounts within the housing which separate and absorb vibrations of the motor within the housing and a drive disk of a moderately soft material, which is firm enough to transfer torque from the motor to the roller while being soft enough to absorb vibrations which would otherwise be transmitted from the motor to the roller. An interconnect mounting the drive disk to the drive shaft of the motor is also made of a third relatively soft material, which is harder than the drive disk to more ably transmit torque but soft enough so as not to unduly transmit noise.