Pulse pileup events degrade the signal-to-noise ratio (SNR) of nuclear medicine data. When such events occur in multiplexed detectors, they cause spatial misposition, energy spectrum distortion and degraded timing resolution, which leads to image artifacts. Pulse pileup is pronounced in PETbox4, a bench top PET scanner dedicated to high sensitivity and high resolution imaging of mice. In that system, the combination of high absolute sensitivity, long scintillator decay time (BGO) and highly multiplexed electronics lead to a significant fraction of pulse pileup, reached at lower total activity than for comparable instruments. In this manuscript, a new pulse pileup rejection method named position shift rejection (PSR) is introduced. The performance of PSR is compared with a conventional leading edge rejection (LER) method and with no pileup rejection implemented (NoPR). A comprehensive digital pulse library was developed for objective evaluation and optimization of the PSR and LER, in which pulse waveforms were directly recorded from real measurements exactly representing the signals to be processed. Physical measurements including singles event acquisition, peak system sensitivity and NEMA NU-4 image quality phantom were also performed in the PETbox4 system to validate and compare the different pulse pile-up rejection methods. The evaluation of both physical measurements and model pulse trains demonstrated that the new PSR performs more accurate pileup event identification and avoids erroneous rejection of valid events. For the PETbox4 system, this improvement leads to a significant recovery of sensitivity at low count rates, amounting to about 1/4th of the expected true coincidence events, compared to the LER method. Furthermore, with the implementation of PSR, optimal image quality can be achieved near the peak noise equivalent count rate (NECR).