The crystallization and melting transitions for tetracontane in propane, measured in this work at pressures up to about 1200 bar, are found to exhibit a temperature minimum, which implies crystallization upon decompression (retrograde crystallization). The supercooling effect, which is the difference between the crystallization and melting temperature, is found to decrease with increasing tetracontane concentration. The transitions induced by varying temperature at constant pressure are found to fall near the same curve as those induced by varying pressure at constant temperature. The difference between the crystallization and melting pressure represents the super-compression effect.