A rack-serving unit for storing boxes having an open box bottom, including a load pick-up device and at least one substantially horizontally telescopic article transport gripper including at least one rest for the articles for gripping under an article, is provided with a single telescopic gripper pin serving as article transport gripper and having a rest for the articles for gripping under the article in a just unstable position and at least one telescopic flank and/or a telescopic hold-down device for setting a stable transport position of the gripped article. In an order-picking warehouse equipped with said rack-serving unit having storing boxes with bottoms which are open in the center thereof, the telescopic gripper pin includes a rest for the articles of a width which is transverse to the telescoping direction for supporting the article in a just unstable position on the rest for the articles and the box bottom opening being just slightly broader than the width.