Disclosed is a set of inks for printing multicolor images in an ink jet printer, said ink set comprising (A) a first ink having a first color and comprising water and a colorant selected from the group consisting of (1) anionic dyes, (2) dyes having physically or chemically associated therewith a stabilizing agent having anionic groups thereon, (3) pigment particles having anionic groups chemically attached thereto, (4) pigment particles having physically or chemically associated therewith a stabilizing agent having anionic groups thereon, and (5) mixtures thereof; and (B) a second ink comprising water, an optional colorant having a color other than the first color, and an ammonium salt having at least two cationic ammonium functional groups, wherein the colorant in the first ink is capable of being immobilized on a printing substrate by interaction with the ammonium salt having at least two cationic ammonium functional groups in the second ink, thereby enabling reduced intercolor bleed.