A method for producing mechanical pulps which are useful for producing coated light weight paper, magazine paper and the like, is disclosed, which includes preheating lignocellulose-containing material in the presence of impregnation chemicals, refining the preheated lignocellulose-containing material utiilizing a pair of counter-rotating refining discs under pressure, bleaching the thus produced partially refined lignocellulose-containing material, and refining the bleached material in a second refining step utilizing a pair of refining discs, one of which is stationary and the other which is rotating under pressure.