One of the problems encountered in designing a waveguide free‐electron laser (FEL) is to suppress the lower‐frequency branch, which may have a higher gain than the more useful higher‐frequency branch. It is shown that the electron pulse length and energy spread strongly influence the competition between the gains at high and low frequency for a waveguide FEL. It is also found that the negative slippage that may take place at the lower‐frequency branch results in larger reduction in gain than the positive slippage. The maximum allowable electron energy spread for both resonance frequencies is derived. ©1995 American Institute of Physics.