We investigate a new problem for linear control systems: find a stabilizing state feedback controller which depends on a small number of states or a static output feedback which depends on a small number of outputs. Such problem formulations are motivated with various real-life applications. The tool for solution is L1 optimization technique combined with LMI approach. Simulation results are highly promising, they demonstrate that the number of states or outputs for use in control can be strongly reduced without serious losses in performance.