This paper addresses the problem of integrated design of autonomous underwater vehicle (AUV) plant parameters and feedback controllers to meet mission performance requirements with minimum energy expenditure. This research topichas been motivated by the fact that significant energy savings and increased dynamic performance can in principle be obtained if the process of control system design is integrated with the design of the vehicle itself, thus departing considerably from the classical approach whereby the plant structure is essentially fixed a priori. As a first step towards the solution of this general problem, the following simpler problem is addressed and solved: given an AUV (with a fixed baseline configuration) that is required to operate over a finite set of representative trim conditions in the vertical plane in the course of a given mission scenario, determine the optimal size of the bow and stern planes so that the average propulsion power required to execute that mission is minimized. The minimization process is subjectto open-loop stability requirements, and to theexistence of stabilizing feedback controllers that can meet time and frequency closed-loop requirements about each trim condition. The paper introduces a methodology to solve this combined plant controller optimization problem in the framework of convex optimization theory and describes its application to theselection of the optimal size of bow and stern planes for a prototype autonomous vehicle.