A new method for preventing pulse pileup in scintillation detectors is proposed. In the new method (G-INT), the energy of an event is calculated from the 'gated integral' of the pulse signal and the period of integration. The period of integration is not fixed but is shortened by the arrival of the succeeding pulse so as to avoid post-pulse pileup. The effect of pre-pulse pileup is corrected by subtracting the remnant energy of the preceding pulses, which is calculated from the gated integral of the preceding pulse. To avoid error due to short pulse intervals, pre- and post-pulse deadtimes are imposed. The method is similar to Wong's method (W-SUM) that depicts the energy by the 'weighted sum' of the current signal and the integrated signal. The performance of G-INT has been studied by Monte Carlo simulation in comparison with W-SUM, the variable sampling-time technique and simple delay-line clipping. It is shown that G-INT provides the smallest degradation in pulse height resolution for a given count rate capability. The difference between G-INT and W-SUM is explained by the difference in the amount of statistical noise involved in the gated integral and in the weighted sum.