A laundry washing machine comprising an outer casing and, inside said outer casing, a washing tub, a rotatable drum housed in axially rotatable manner inside the washing tub and structured for housing the laundry to be washed, a detergent dispenser which is structured for supplying detergent into the washing tub, a fresh-water supply circuit which is structured for selectively channelling a flow of fresh water from the water mains towards the detergent dispenser and/or the washing tub, and an internal water softening device capable of reducing the hardness degree of the fresh water that the fresh-water supply circuit channels towards the detergent dispenser or the washing tub; the laundry washing machine furthermore comprising: at least a first drawer (16, 70) which is fitted/inserted in extractable manner into a corresponding drawer housing (18, 71) located/recessed inside the outer casing; a substantially basin-shaped, regeneration-agent compartment which is located into said first drawer (16, 70) and is structured for being manually fillable with a given amount of consumable salt or other regeneration agent; and a water-supply line which is structured for selectively channelling a flow of fresh water of the water mains into said regeneration-agent compartment to form brine; wherein the regeneration-agent compartment comprises a brine the laundry washing machine being characterized in that: the brine outlet is a pass-through opening formed on the bottom of the regeneration-agent compartment and is shaped/dimensioned to allow the brine formed inside the regeneration-agent compartment to freely fall on the bottom of the drawer housing (18, 71); the laundry washing machine additionally comprising a partitioning septum which extends inside the regeneration-agent compartment between a water inlet fluidically communicating with said water-supply line and the brine outlet of the regeneration-agent compartment, and has a water-permeable structure which is designed to slow down the outflow of the brine from the regeneration-agent compartment via the brine outlet for causing a temporary stagnation of the water above the partitioning septum to improve the salt dissolution, wherein the water-permeable partitioning septum extends inside the regeneration-agent compartment, horizontally and parallel to the bottom of the regeneration-agent compartment, and spaced from the bottom of the regeneration-agent compartment so as to form an air gap immediately above the bottom of said regeneration-agent compartment. the laundry washing machine furthermore comprising: at least a first drawer (16, 70) which is fitted/inserted in extractable manner into a corresponding drawer housing (18, 71) located/recessed inside the outer casing; a substantially basin-shaped, regeneration-agent compartment which is located into said first drawer (16, 70) and is structured for being manually fillable with a given amount of consumable salt or other regeneration agent; and a water-supply line which is structured for selectively channelling a flow of fresh water of the water mains into said regeneration-agent compartment to form brine; wherein the regeneration-agent compartment comprises a brine the laundry washing machine being characterized in that: the brine outlet is a pass-through opening formed on the bottom of the regeneration-agent compartment and is shaped/dimensioned to allow the brine formed inside the regeneration-agent compartment to freely fall on the bottom of the drawer housing (18, 71); the laundry washing machine additionally comprising a partitioning septum which extends inside the regeneration-agent compartment between a water inlet fluidically communicating with said water-supply line and the brine outlet of the regeneration-agent compartment, and has a water-permeable structure which is designed to slow down the outflow of the brine from the regeneration-agent compartment via the brine outlet for causing a temporary stagnation of the water above the partitioning septum to improve the salt dissolution, wherein the water-permeable partitioning septum extends inside the regeneration-agent compartment, horizontally and parallel to the bottom of the regeneration-agent compartment, and spaced from the bottom of the regeneration-agent compartment so as to form an air gap immediately above the bottom of said regeneration-agent compartment.