Disclosed is a set of inks for printing multicolor images in an ink jet printer, said ink set comprising (1) a first ink having a first color and comprising water and an anionic dye; and (2) a second ink having a second color different from the first color and comprising (a) water, and (b) pigment particles having chemically bonded to the surfaces thereof moieties containing amine or quaternary amine functional groups, wherein the anionic dye in the first ink is capable of being immobilized on a printing substrate by interaction with the pigment particles in the second ink, thereby enabling reduced intercolor bleed.