Methods are disclosed for the purification of crude compositions comprising 2,5-furandicarboxylic acid, dimethyl ester (FDME) or other diester derivatives (e.g., dialkyl ester derivatives) of 2,5-furandicarboxylic acid (FDCA), by crystallization. In this regard, certain solvents, and classes of solvents, have been discovered to promote the selective crystallization of FDME over impurities often generated in its production by FDCA esterification and other upstream processing steps. Importantly, certain impurities that are selectively removed include those that would otherwise be detrimental to the color and/or color stability of the purified composition. Other improvements in crystallization reside in the use of techniques such as liquid-liquid extraction and pre-treatment of the crystallization solution by contact with a solid medium.