Steam wrinkle-removing appliance comprising a water tank (110) in direct communication with a steam-producing boiling chamber (60), said boiling chamber (60) comprising a heating unit (4) and a steam outlet (62) through which the steam can freely flow toward a wrinkle-removing element such as a steam brush, characterized in that the boiling chamber (60) is supplied with water from the tank (110) by means of several supply lines (70) with a small flow cross-section of less than 15 mm2, said supply lines extending lengthwise between an end (70A) opening into the tank (110) and an end (70B) opening into the boiling chamber (60) so as to generate head losses that limit the backflow of hot water or steam toward the tank (110).