An improved process for the manufacture of alkaline bleaching compositions, especially liquid and/or gel compositions of high solubility and low abrasiveness, useful to the consumer, especially as products for hard surface cleaning, bleaching or disinfectancy. The products are made by a three-stage process and comprise particular chlorine and bromine bleach sources and particular aminofunctional materials such as low-impurity sulfamate. The process has mixing sequences and starting ingredient selections which provide unexpectedly improved product