A laundry washing machine equipped with a treating agents dispenser includes a drawer having at least one open-top compartment and a water distributor arranged above the drawer. The water distributor includes at least one water conveying line for conveying water to a region of the water distributor positioned above the at least one compartment. The water conveying line comprises a first path which supplies with water one or more first outlets arranged in the region and a second path which supplies with water one or more second outlets suited to convey water to the tub/drum bypassing the at least one compartment. A common path portion is shared by the first path and the second path. In a second aspect, first and second water conveying lines extend from hot and cold water sources respectively, to a drawer compartment, without cross-linkage to other water distributor lines therebetween.