We demonstrate the three-fold post-chirped-pulse-amplification (post-CPA) pulse compression of a high peak power laser pulse using allyl diglycol carbonate (CR39), which was selected as the optimal material for near-field self-phase modulation out of a set of various nonlinear plastic materials, each characterized with respect to its nonlinear refractive index and optical transmission. The investigated materials could be applied for further pulse compression at high peak powers, as well as for gain narrowing compensation within millijoule-class amplifiers. The post-CPA pulse compression technique was tested directly after the first CPA stage within the POLARIS laser system, with the compact setup containing a single 1 mm thick plastic sample and a chirped mirror pair, which enabled a substantial shortening of the compressed pulse duration and, hence, a significant increase in the laser peak power without any additional modifications to the existing CPA chain.