This paper deals with the design of robust digital controllers by the combined pole placement/sensitivity function shaping method. The problem of assigning a desired region for the closed-loop poles and simultaneously respecting certain bounds on the sensitivity functions is formulated and solved as a convex optimization problem. Specifications like dominant closed-loop poles or integration controller action may be introduced just as well as other fixed parts for the controller. The method is illustrated by the controller design for a very flexible 360 degrees arm.