For measurements of the statistical distribution of parameters of pulses (peak amplitude, etc.), a technique is introduced to measure accurately the background due to pulses not correlated in time to the events of interest. This technique is applicable when an event marker signal, correlated in time to the events of interest, is available, i.e., always in time measurements and often in other cases. The basic principle is to make cycles of two successive measurements, in which the probability of measuring a background pulse is the same for both, while the one of measuring an event pulse is much higher in the first measurement; the results of the two measurements must be treated differently. The technique and its applications to amplitude and time measurements are considered in detail. The instrument developed is presented together with some experimental results.