In view of a quantum electrodynamics test, a "double" free-electron laser (FEL) oscillator is proposed as a possible device for head-on photon-photon collisions in vacuum. The oscillator is conceived in order to produce two laser beams in the same cavity by two counterpropagating electron beams. The latter are in turn exploited to produce gamma photons by backward Compton scattering of the intracavity FEL radiation itself. In view of an effective device design, specific ranges of values for the various parameters, that characterize the system, are individualized for operation at the maximum of the γ-γ scattering cross section. An estimate of the collision rate in definite device configurations is provided. © 2013 Optical Society of America.