The invention relates to the operation of an energy-focusing and solid-angle-focusing reflector for time-of-flight mass spectrometers with pulsed ion acceleration into a flight tube, e.g. from an ion source with ionization by matrix-assisted laser desorption (MALDI). The objective of the invention is to generate high mass resolution in wide mass ranges up to high masses above eight kilodaltons by varying at least one operating voltage on one of the diaphragms of the reflector which can be varied according to a suitable time function during the spectrum acquisition. It may also be advantageous to adapt the operation of the accelerating voltages in the starting region of the ions accordingly. These measures make it possible to achieve a mass resolution much higher than R=100,000 in a wide mass range extending up to and above eight kilodaltons.