Abstract: A filter device for brewing beverages from coffee or tea grounds has a support frame comprising a first annular member and at least two radially outwardly projecting supports for placing the filter device onto a rim of a beverage container. The first annular member has a diameter smaller than the diameter of the beverage container. A disposable filter insert enclosing an amount of coffee grounds or tea leaves for brewing a beverage in the beverage container is provided. The filter insert has a seamless conical porous pocket for receiving the coffee grounds or tea leaves. The conical pocket has a cone base facing upwardly and a cone top facing downwardly. The filter insert also has a porous cover covering an opening at cone base. The pocket has finer pores than the cover. The cover sags downwardly and forms a depression.