In order to achieve high accurate pointing with robustness to system uncertainty, inertial Line of Sight stabilization loop controllers are designed with a specific structure related to the nature of the disturbances to be rejected. For this problem, H∞ Loop Shaping synthesis is efficiently used, but the resulting controllers are of high order because of the order of the synthesis model and weighting filters which are useful to shape the loop regarding synthesis objectives. In this paper, reduced order controllers are investigated through recently developed tools that recast the fixed order H∞ synthesis problem as a nonsmooth optimization problem.