A steam head for a garment steamer includes a handle, and a steam duct having an upstream end connectable to a steam hose and a downstream end that defines a steam ejection opening with a circumferential edge that forms a frontal contact surface. A surface area of the frontal contact surface is smaller than an area of the steam ejection opening. The steam head further includes a drainage tube extending between condensate inlet and outlet ends, where the condensate inlet end is disposed within a downstream portion of the steam duct while the condensate outlet end is disposed elsewhere, such as connected to a water reservoir or a boiler of the garment steamer, or to a dedicated condensate collector.