Disclosed is a method for purifying aromatic dicarboxylic acid such as isophthalic acid or terephthalic acid. The process treats a crude carboxylic acid (CCA) composition by feeding a CCA composition comprising a liquid and a solid to a filter cake formation zone to form a CCA wet cake composition and a first mother liquor stream; dewatering said CCA wet cake composition to form a dewatered CCA wet cake composition having a second liquid level that is lower than the first liquid level or having no liquid level and a second mother liquor stream; and washing the dewatered CCA wet cake composition with a wash stream in a wash zone to forma washed CCA wet cake composition and a wash liquor stream.