The present disclosure provides a black ink-jet ink, having a pH greater than 7, comprising a first aqueous vehicle, a carbon black pigment, and an amphoteric polymeric dispersant, wherein the amphoteric polymeric dispersant is a block copolymer comprising an A block and a B block, wherein the A block is a segment consisting essentially of an amine monomer; and the B block is a segment comprising an acidic monomer and at least one hydrophobic monomer; wherein the dispersant is neutralized, and with the proviso that the acid number is greater that the amine number, and the B block does not contain an amine monomer. The disclosure further pertains to an ink set comprising this black ink and at least a second ink which contains a reactive species with appropriate cationic agent, salt, or pH capable of destabilizing the carbon black dispersion. Still further, the disclosure pertains to a method of printing wherein the black ink and second ink are printed in an adjacent relationship, thereby minimizing penetration, feathering and/or bleed of the black pigment and improving print quality.