A wrist mechanism for an instrument used in minimally invasive medical procedures employs only four drive cables for control of the pitch, yaw, and grip of an effector. To reduce part count, no pulleys are used. Instead, solid surfaces of clevises in the wrist mechanism cradle the drive cables and are curved in multiple directions to maintain a fixed moment arm for cable torques and eliminate the need for large cable wrap angles. Further, the stiffness of each of the four drive cables can be controlled for improved clinical performance. In particular, the stiffness of the two drive cables that cause grips to close can be greater than the stiffness of the remaining two drive cables that cause the grips to open. The arrangement can minimize cable slack, improving fidelity of motion.