Double output cavities have been used experimentally to increase the efficiency of high-power klystrons [l]. We have used particle-in-cell simulations with the 2+1/2 dimensional code MASK to optimize the design of double output cavities for the lasertron under development at SLAC. We discuss design considerations for double output cavities (e.g., optimum choice of voltages and phases, efficiency, wall interception, breakdown). We describe how one calculates the cavity impedance matrix from the gap voltages and phases. Some results of the effect of varying voltage, perveance, and pulse length are reported. * Work supported by the Department of Energy, contract DE-A CO3-76s F005 15. Pll I (e,, is the phase shift with the origin when both gaps are shorted.) If we assume that the second cavity is tuned near resonance we can take the cot es8 term to be zero. Then: x12 = f (x11 x22)1'2 * (3) These conditions, combined with the two voltages and two currents, completely define the impedance matrix.