A detailed investigation of piezoelectric ringing and resonance effects in beta barium borate (BBO)-crystal-based Pockels cells in a pulse picker device is presented. Measurements mapping piezoelectric oscillation amplitude distribution in the aperture of BBO crystal are also performed. It is determined that in BBO Pockels cells, due to piezoelectric ringing and related effects, the optical contrast ratio is reduced by six to 70 times at certain (resonance) frequencies. Moreover, we demonstrate that in our pulse picker device, which uses a special sequence of control pulses (regeneration method) for the Pockels cell, at certain high-voltage control signal durations, piezoelectric oscillations can be suppressed, which significantly improves performance of the Pockels-cell-based laser pulse picker device at resonance frequencies: in such cases, the optical contrast ratio is stable and higher than 1000:1. Numerical simulation results support the experimental data.