The selective harmonic elimination PWM (SHEPWM) method is systematically applied for the first time to multilevel series-connected voltage source PWM inverters. The method is implemented based on optimization techniques. The optimization starting point is obtained using a phase-shift harmonic suppression approach. Another less computationally demanding harmonic suppression technique, called a mirror surplus harmonic method, is proposed for five-level (double-cell) inverters. Theoretical results of both methods are verified by experiments and simulations for a double-cell inverter. Simulation results for a five-cell (11-level) inverter are also presented for the multilevel SHEPWM method.