The invention relates to methods and devices for measuring daughter ion spectra (also called fragment ion spectra or MS/MS spectra) in time-of-flight mass spectrometers with orthogonal injection of the ions. The invention filters the parent ions selected to be fragmented by a mass filter before they are injected into the time-of-flight mass spectrometer, fragments the selected ions in a first stage of the time-of-flight mass spectrometer within a collision cell filled with collision gas at collision energies between one and five kiloelectron-volts, further accelerates the fragment ions and measures the fragment ions in a second stage of the time-of-flight mass spectrometer.