Abstract: A teat unit for use when dispensing directly into the mouth from a fluid-containing disposable package of a thin sheet-shaped plastic or cardboard material. The teat unit includes an upwardly extending teat part, an intermediate radial flange and a downwardly extending insertion part. The insertion part has structure for holding the teat unit in position during dispensing with the radial flange having a downwardly facing side in engagement with the top side of the package, and structure for puncturing the top side of the package through an exposed opening in the top side of the package. The radial flange is shaped as a cover plate having substantially the same extent as the area of the top side of the package for the package size with which the teat unit is to be used, and the holding structure is adapted to hold the cover plate to bear against the top side of the package and to hold the top side of the package in direct sealing engagement with the downwardly facing side of the cover plate.