An aqueous coating composition comprising at least one cathodically depositable binder and optionally at least one crosslinking agent, the coating composition having a pH in a range from 4.0 to 6.5, for at least partly coating an electrically conductive substrate with an electrocoat material, characterized in that the coating composition comprises a total amount of at least 130 ppm of bismuth, based on the total weight of the coating composition, including at least 30 ppm of bismuth, based on the total weight of the coating composition, in a form in which it is in solution in the coating composition, and optionally at least 100 ppm of bismuth, based on the total weight of the coating composition, in a form in which it is not in solution in the coating composition, and the coating composition further comprises at least one at least bidentate complexing agent suitable for complexing bismuth, the at least one complexing agent being a compound of the general formula or an anion of said compound in which R 1 is a C 1-6 aliphatic radical substituted by at least one OH group, m is 0 or 1, R a and R b in each case independently of one another are selected from the group consisting of H and C 1-6 aliphatic radicals, optionally substituted by at least one OH group, R 2, R 3, R 4, and R 5 in each case independently of one another are H or are a C 1-6 aliphatic radical optionally substituted by at least one OH group, n is 1 or 2, o is 1 or 2, p is 0, 1, 2, or 3, and R 6 is C(=O)OH, S(=O) 2 OH, P(=O) 2, NR 7 R 8, or a C 1-6 aliphatic radical which is substituted by at least one OH group, where R 7 and R 8 in each case independently of one another are selected from the group consisting of H and C 1-6 aliphatic radicals which are optionally substituted by at least one OH group, with the proviso that at least one of the radicals R 7 and R 8 is a C 1-6 aliphatic radical which is substituted by at least one OH group. at least one cathodically depositable binder and optionally at least one crosslinking agent, at least 30 ppm of bismuth, based on the total weight of the coating composition, in a form in which it is in solution in the coating composition, and optionally at least 100 ppm of bismuth, based on the total weight of the coating composition, in a form in which it is not in solution in the coating composition, and at least one at least bidentate complexing agent suitable for complexing bismuth, R 1 is a C 1-6 aliphatic radical substituted by at least one OH group, m is 0 or 1, R a and R b in each case independently of one another are selected from the group consisting of H and C 1-6 aliphatic radicals, optionally substituted by at least one OH group, R 2, R 3, R 4, and R 5 in each case independently of one another are H or are a C 1-6 aliphatic radical optionally substituted by at least one OH group, n is 1 or 2, o is 1 or 2, p is 0, 1, 2, or 3, and R 6 is C(=O)OH, S(=O) 2 OH, P(=O) 2, NR 7 R 8, or a C 1-6 aliphatic radical which is substituted by at least one OH group, where R 7 and R 8 in each case independently of one another are selected from the group consisting of H and C 1-6 aliphatic radicals which are optionally substituted by at least one OH group, with the proviso that at least one of the radicals R 7 and R 8 is a C 1-6 aliphatic radical which is substituted by at least one OH group.