A process for converting perylene-3,4:9,10-tetracarboximides of the general formula I in which R1 and R2 are each unbranched, branched or cyclic C1-C8-alkyl to a form suitable for use as fluorescent dyes, which comprises a) dissolving or suspending the perylene-3,4:9,10-tetracarboximides in an organic or inorganic solvent whose molecules have a molecular volume of ≦230 Å3 at from 0 to 250° C., b1) cooling the solution obtained in step a) to or below the crystallization temperature and, in the case of an organic solvent, if desired at the same time removing excess solvent until the first crystals form, or, in the case of an inorganic solvent, adding water or dilute aqueous solutions of the solvent until the first crystals form, and maintaining the solution at this temperature for further crystallization or b2) cooling the suspension obtained in step a) to or below the crystallization temperature when the temperature in step a) was above the crystallization temperature, and maintaining the suspension at this temperature for further crystallization, c) isolating the solvate crystals formed in step b) and d) then removing the solvent from the solvate crystals, and also novel crystalline forms of perylene-3,4:9,10-tetracarboxylic diimides.