When taking beta-ray spectra by semiconductor detector techniques it is of advantage to stack several detectors in series. The resolution of a single detector determines the optimum resolution of the stack-assembly. However, such a system involves also the possibility of spurious counts. These edge effects cause an additional deterioration of the resolution. To take best out of the resolution of the detectors a trigger-circuit was developed, to exclude the spurious pulses from entering the pulse-height analyzer. A coincidence-anticoincidence-circuit discriminates against the unwanted pulses. The pulses so selected are fed to the input gate of the PHA. In this way the resolution of the spectrometer is improved. Moreover, the background counts are reduced to a minimum value. This is of importance when analyzing sources of low activities.