In a mass spectrometer, sample ions are produced by using matrix assisted laser desorption with a matrix substance that supports spontaneous, non-ergodic ISD fragmentation and a laser light source with nanosecond light pulses and a multiple spot beam profile. A plurality of individual time-of-flight spectra are recorded from the resulting ions in such a way that amplification of ion signals in the mass spectrometer detector is initially reduced so that only ions with masses near a mass range limit are initially recorded. During the repeated acquisitions of the individual time-of-flight spectra, both the detector amplification and the mass range limit are increased. By these methods, it is possible to evaluate c and z fragment ions in lower mass ranges and to directly read N-terminal sequences from near terminus up to 80 amino acids and beyond, and C-terminal sequences up to more than 60 amino acids.