This article reports a novel experimental technique, namely, the foil cycling technique, developed on the VESUVIO spectrometer ͑ISIS spallation source͒ operating in the resonance detector configuration. It is shown that with a proper use of two foils of the same neutron absorbing material it is possible, in a double energy analysis process, to narrow the width of the instrumental resolution of a spectrometer operating in the resonance detector configuration and to achieve an effective subtraction of the neutron and gamma backgrounds. Preliminary experimental results, obtained from deep inelastic neutron scattering measurements on lead, zirconium hydride, and deuterium chloride samples, are presented.