A dielectric cover system for an insulator supporting a high voltage conductor is molded to fit over the insulator to cover at least a top portion of the insulator and the conductor in contact with the insulator. A bolt through the cover is inserted to a depth to engage a reduced-diameter neck area of the insulator to prevent the cover from being rotated about the insulator during a high wind condition. Other securing devices may instead be used that allow the cover to be freely placed over the insulator and then effectively restrict an inner diameter of the cover at a reduced diameter portion of the insulator, such that the securing device blocks the cover from being lifted off the insulator and rotated about the insulator.