Broadband dielectric measurements on leucrose were performed under ambient and high pressure. We showed that in this disaccharide, there are two secondary relaxation modes, a slower one sensitive to pressure and a faster one that is not. This finding clearly indicates that the faster secondary relaxation originates from the intramolecular motion. This conclusion contradicted previous interpretations of this mode observed for trehalose and maltitol, systems very closely related to leucrose. In addition, pressure sensitivity of the slower relaxation confirms our recent interpretation about the character of this process. Furthermore, we discovered that unlike the faster relaxation, the slower secondary relaxation is sensitive to the thermodynamic history of measurements. Finally, monitoring the changes in maximum loss of the slower secondary relaxation measured at the same pressure and temperature conditions for glasses obtained via different thermodynamic routes enabled us to draw a conclusion about the density of the formed glasses. Our observations may be helpful in establishing a new method of suppressing crystallization of amorphous drugs.