Control-moment gyroscopes (CMGs) are power-efficient attitude-control actuators that produce high torques for agile spacecraft. We propose the use of CMGs in actuating joint degrees of freedom in a spacecraft-mounted agile imaging payload, whose tasks include acquiring and tracking a high-speed target. High agility, on the order of several radians per second, characterizes the system of interest here; however, such capabilities are achieved with traditional actuators only at the expense of excessively high electrical power. The proposed design provides agile slewing of an imaging payload for a very small fraction of the power required by fixed rotors in a reaction wheel assembly. This study provides a dynamics analysis for a general system, but we focus on an example in which the inertia dyadics are spherical. We demonstrate by simulation that a CMG-driven system offers the same agility with less than 1% of the power of a telescope actuated by reaction wheels.