Quantum theory is applied to interference of emission and absorption i
n a two-section Cerenkov free-electron laser (FEL). A scheme for absor
ption cancellation with enhanced gain, which resembles ''lasing withou
t inversion'' in atomic systems, is proposed. This scheme is based on
the adjustment of the phases of electrons and light by appropriate dis
persion between the two sections. It enables FEL operation even with a
broad electron momentum spread. Such a scheme is interesting in the c
ontext of EEL operation in the ultraviolet and X-ray regimes.