The present invention relates to a cover device for a drink container such as a glass or cup, comprising: - a cover member for covering at least a part of the upper side of the drink container, - at least one opening and/or gap arranged in the cover member for passage of drink and/or air, - a fastening member for removably fastening the cover device onto the drink container, wherein - the cover device can be placed over an opening of the drink container in a manner such that the cover member can be arranged substantially over the opening and the fastening member can be arranged against at least one wall of the drink container. The invention also relates to a method for the use of such a cover device.