An improved design for the backshell of a connector for a shielded, multiple-wire cable reduces the size of the backshell, relative to traditional designs of backshells of otherwise identical cable connectors. Notwithstanding the reduction in size, the design provides all the functionality typically demanded of such a backshell, including (1) termination of the cable shield (that is, grounding of the shield to the backshell), (2) strain relief for the cable, and (3) protection against electromagnetic interference (EMI). A traditional backshell design provides for termination of the cable shield inside the backshell. To accommodate the shield, the interior of the backshell must contain wasted volume and, consequently, must be larger than would otherwise be necessary. The present improved design provides for termination of the cable shield on the outside of the backshell, thereby eliminating the need for wasted interior volume and enabling a reduction in size. In particular, the backshell is now only about one-third as large as a corresponding traditional backshell.