A pressurized drive coupling includes a socket joined to an end of one shaft in a drive system and a stem extending from an end of another shaft. The stem is insertable into a cavity formed in the socket and the stem and cavity have mating noncircular transverse cross-sections. A sleeve is seated around the socket. The sleeve includes a rigid outer section and a deformable inner section which is in contact with the socket. A pressure chamber is formed between the sections of the sleeve and the pressure chamber is filled with a suitable fluid which is pressurized to reduce the dimensions of the cavity and eliminate clearance between the stem and cavity.