A beverage machine having a height-adjustment device that includes a movable support plate for adjusting the position of the recipient relative to at least one beverage outlet. The support plate is movable relative to the at least one beverage outlet. The machine also includes a displacement mechanism for displacing the support plate relative to the outlet. The displacement mechanism includes a motorized driver for driving the displacement mechanism, a controller for controlling the actuation of the driver and which is configured to set a predetermined distance between the outlet and the recipient. A drip-collecting device can also be selectively provided to collect liquid falling from the beverage outlet when the recipient is not present.