Abstract: A method of making bleached mechanical pulps is disclosed for pulping mills having a primary and a secondary refiner. A first step is to provide cellulosic materials, such as wood chips to refine into the pulp; the wood chips have an initial brightness level. A second step is to provide a bleaching liquor to the refining system of the pulp mill, wherein the liquor comprises an amount of hydrogen peroxide and an amount of alkali having greater than 0% to 100% magnesium hydroxide or soda ash or a combination thereof. A third step is to hold the pulp with the bleaching liquor at a temperature in the range of about 85° to about 160° C. and for about 2 to about 180 minutes.