To make a lamp of quartz or hard glass which has a bulb (10, 22) which doesot have an exhaust tip, for example a metal halide high-pressure discharge lamp or a halogen incandescent lamp, the glass bulb is formed by blow-molding the bulb to the desired shape, then retaining an electrode system having electrodes (14, 14a) to be placed in the bulb, current supply leads (12, 24) extending externally of the bulb, and sealing foils (13, 23) connecting the current supply leads to the electrodes in a holder die (11, 25), introducing the electrodes by moving the holder die towards the bulb, flushing the bulb by introducing and selectively removing flushing gas through an open end of the tube, introducing a measured quantity of a fill substance, such as mercury, an iodide or the like, into the bulb through the open end thereof, and then heating the bulb in the region of the position of the sealing foils and pinch-sealing the bulb. Excess glass is then cut off and the bulb can be supplied with a base. To introduce the fill gas and fill substances, the holder die can be formed with a through-opening through which gas exchange can take place and fill substances, for example in form of pellets or pills introduced. The pinch-sealing can be carried out in two steps, one step pinch-sealing the electrode system but leaving capillary openings (62) adjacent the side walls of the tube to permit gas exchange. The capillaries can then be melted shut by a pointed flame.