Free radical heavy metal ions in water-soluble heavy metal complex dyestuffs are removed from the synthesis solution of the heavy metal complex dyestuff by means of a compound or several of the compounds mentioned below:(a) saturated and unsaturated fatty acids having about 8 to 18 carbon atoms and water-soluble salts thereof;(b) the monoesters and diesters of orthophosphoric acid and salts thereof corresponding to the general formula (1a) and (1b) ##STR1## in which R denotes a saturated or unsaturated aliphatic radical having about 8 to 18 carbon atoms and M stands for a hydrogen atom or a salt-forming, water-solubilizing metal;(c) aliphatic sulfonic acids and water-soluble salts thereof corresponding to the general formula (2)R--SO.sub.3 M (2) in which R and M have the abovementioned meanings;(d) aliphatic phosphonic acids and monoesters thereof and also water-soluble salts thereof corresponding to the general formulae (3a) and (3b) ##STR2## in which R and M have the abovementioned meanings; (e) malonic acid and water-soluble salts thereof;(f) trimercapto-s-triazine, 2-aminobenzoic acid, 8-hydroxyquinoline and water-soluble salts of these compounds;(g) water-soluble sulfides, in particular alkali metal sulfides;(h) functionalized water-insoluble polymers which react with metal ions by the ion-exchanger principle or form metal chelate complexes.Using these compounds, the excess heavy metal ions are precipitated out of the synthesis solution or separated off, without the heavy metal ions bound as a complex in the dye being attached.