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We investigate the design of MIMO linear precoders for multiuser broadcast channels under signal leakage constraints. This power leakage constraints reflect both an important security consideration and the need for interference suppression at receivers. Defining a convex optimization problem, we propose two sequential semi-definite program algorithms. In principle, our algorithms exploit both spatial diversity and multiuser diversity to enhance the overall system performance. The resulting MIMO precoded transmission demonstrates superior performance over time-division multiplexed multiuser transmission in conjunction with the traditional space-time transmission.