The invention provides methods and apparatus for tandem mass spectrometry (MS/MS) in which parent ions generated from a sample are passed through a mass filter (2) and are fragmented into daughter ions in fragmentation means (3), the daughter ions being passed through a discontinuous output mass analyser, such as a time-of-flight analyzer (16) or an ion storage device (29). The range of possible parent mass-to-charge ratios is split into a plurality of smaller ranges, and the mass filter (2) is set to pass ions of each smaller range in turn. A flag is set for each smaller range which produces daughter ions of interest, and the mass filter (2) is set to pass each mass-to-charge ratio of the flagged ranges so that the mass-to-charge ratios of the fragmented ions produced for each of the mass-to-charge ratios passed may be determined using the discontinuous analyser (16, 29). The flagged ranges may be themselves split into a plurality of still smaller ranges, which are correspondingly flagged.