The present disclosure relates to a cathodically depositable aqueous electrodeposition coating material including at least one epoxide-amine adduct (a), at least one pigment and/or at least one filler (b), and at least one crosslinking agent (c), a fraction of at least 25 wt % of the crosslinking agent (c), based on the total weight of the crosslinking agent (c), being formed by at least one tris(alkoxycarbonylamino)-1,3,5-triazine; to a method for coating an electrically conductive substrate by cathodic electrodeposition coating using said electrodeposition coating material; to a substrate coated accordingly; and also to a use of a tris(alkoxycarbonylamino)-1,3,5-triazine in a cathodically depositable electrodeposition coating material for reducing or eliminating the sensitivity to disruption of the electrodeposition coating bath toward impurities present therein through phosphates and/or through other metal salts which have been carried into the electrodeposition coating bath as a result of pretreatment steps ahead of the electrodeposition coating.