An aqueous polishing agent, comprising at least one type of solid polymer particles which are finely dispersed in the aqueous phase and contain functional groups capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished and - forming strong complexes with the metal of the surfaces to be polished as an abrasive; at least one organic non-polymeric compound which is dissolved in the aqueous phase and capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming strong, water-soluble complexes with the said metal, and - causing an increase of the material removal rate MRR and the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent as a hard complexing agent; and at least one organic non-polymeric compound which - is completely dissolved and does not form a separate solid or liquid phase in the aqueous phase - is capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming slightly soluble or insoluble complexes with the metal of the surfaces to be polished, which complexes are capable of being adsorbed by the metal surfaces to be polished, and - causing a lower increase of the material removal rate MRR than the compound and a lower increase of the static etch rate SER than the compound or no increase of the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent, and - is selected from the group consisting of dicyandiamide and triazines containing at least one primary amino group as a soft complexing agent. at least one type of solid polymer particles which are finely dispersed in the aqueous phase and contain functional groups capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished and - forming strong complexes with the metal of the surfaces to be polished as an abrasive; - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished and - forming strong complexes with the metal of the surfaces to be polished at least one organic non-polymeric compound which is dissolved in the aqueous phase and capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming strong, water-soluble complexes with the said metal, and - causing an increase of the material removal rate MRR and the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent as a hard complexing agent; and - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming strong, water-soluble complexes with the said metal, and - causing an increase of the material removal rate MRR and the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent at least one organic non-polymeric compound which - is completely dissolved and does not form a separate solid or liquid phase in the aqueous phase - is capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming slightly soluble or insoluble complexes with the metal of the surfaces to be polished, which complexes are capable of being adsorbed by the metal surfaces to be polished, and - causing a lower increase of the material removal rate MRR than the compound and a lower increase of the static etch rate SER than the compound or no increase of the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent, and - is selected from the group consisting of dicyandiamide and triazines containing at least one primary amino group as a soft complexing agent. - is completely dissolved and does not form a separate solid or liquid phase in the aqueous phase - is capable of - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming slightly soluble or insoluble complexes with the metal of the surfaces to be polished, which complexes are capable of being adsorbed by the metal surfaces to be polished, and - causing a lower increase of the material removal rate MRR than the compound and a lower increase of the static etch rate SER than the compound or no increase of the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent, and - interacting with the metal of and/or the metal oxides on top of the surfaces to be polished, - forming slightly soluble or insoluble complexes with the metal of the surfaces to be polished, which complexes are capable of being adsorbed by the metal surfaces to be polished, and - causing a lower increase of the material removal rate MRR than the compound and a lower increase of the static etch rate SER than the compound or no increase of the static etch rate SER of the metal surfaces to be polished with increasing concentration of the compound in the aqueous polishing agent, and - is selected from the group consisting of dicyandiamide and triazines containing at least one primary amino group