A piston-diaphragm assembly for a valve with a piston comprising a stem and a needle. The stem comprises a piston groove with a groove proximal rim. The needle is attached to a stem distal end. The assembly comprises a diaphragm with a peripheral annular ring, an internal annular ring received in the piston groove for attaching the diaphragm thereto, and an annular membrane connecting the annular rings. The needle comprises a crown, which surrounds the stem and externally covers the internal annular ring and which comprises a crown rim, which ends the crown at the groove proximal rim. The diaphragm is radially interposed between the groove proximal rim and the crown rim, being in contact with the crown rim.