Abstract. The CODIF instrument on the Cluster spacecraft is a time-of-flight (TOF) ion mass spectrometer. Although TOF spectrometers are relatively immune to background contamination due to the inherent double coincidence requirement, high background rates can still result in false coincidences. Along the Cluster orbit, false coincidences are commonly observed due to the penetrating radiation of relativistic electrons during the encounters with the Earth's radiation belts. A second type of background in these instruments occurs when events of one species fall into the time-of-flight range defined for another species. Although the fraction of the H+ events that spill into the He+ measurement is small, when the actual He+ fluxes are low this can result in significant contamination. In this paper we present two techniques that allow the subtraction of the false coincidences and the H+ "spill" from the CODIF measurements.