Not all blasters were capable of cutting straight through Stormtrooper's armor. Han Solo's DL-44 "found increased use at the hands of outlaws and fringers on the edge of legality, groups like smugglers and the Rebel Alliance due to its capability to penetrate stormtrooper armor. This caused the Empire to put a restriction order upon this model, restricting and technically outlawing the purchase and ownership of the gun."
everyone knows that.