A constant velocity connection for use in a drill string can include at least one ball-and-socket joint, and an insert rotationally received in an opening formed laterally through a ball of the joint. A method of constructing a constant velocity connection can include installing an insert in an opening formed in a ball of at least one ball-and-socket joint of the constant velocity connection, and allowing the insert to rotate in the opening about a lateral axis. A drill string can include a drilling motor, a drill bit, and a constant velocity connection connected between the drilling motor and the drill bit, the constant velocity connection including at least one ball-and-socket joint, and an insert rotationally received in an opening formed laterally through a ball of the joint.