A high efficiency bleaching method for cellulosic pulp includes: (a) providing a charge of aqueous cellulosic pulp to a bleaching vessel at a consistency of from 10% to 30% along with a peroxy bleaching agent and an alkaline agent effective to adjust pH of the charge to 9.5 to 12.5; and (b) bleaching the aqueous cellulosic pulp in the bleaching vessel while maintaining a bleaching temperature of from 110° F. (43° C.) to 135° F. (57° C.) and a pH of the charge from 9.5 to 12.5 for an extended bleaching retention time. The bleaching method is advantageously used to bleach low brightness recycle pulp, and/or as part of a multistage process with bleaching stages of lesser duration, and/or as a high peroxy efficiency, low dose bleaching process or in connection with concurrently storing and bleaching pulp.