An ink-jet printing
system is disclosed comprising a set of ink-jet inks comprising a first anionic ink comprising an aqueous vehicle, at least one first colorant, and at least one first anionic
polymer; a second anionic ink comprising an aqueous vehicle; at least one second colorant, at least one second anionic
polymer, and an acid additive having a pKa up to the pKa of the at least first
polymer of the first ink; a third cationic ink comprising an aqueous vehicle, at least one third colorant, at least one third cationic polymer, and a pH in the range from about 2 to about 5; and a fourth anionic ink comprising an aqueous vehicle, at least one fourth anionic dye, and a precipitating agent. The printing
system provides improved print quality, specifically, reduced bleed; improved edge-acuity, uniform area fills, and
color quality; while maximizing
lightfastness without sacrificing printing reliability.