A machine and method for making base assemblies for medicine dispensing compresses, includes using a web of substantially imperforate material, and a web of backing material having a base layer with an adhesive on one side to attach the compress to the skin of the user. A plurality of individual foil lids or dam patches are cut from the web of imperforate material, and applied to the adhesive side of the base layer. A release or cover layer is applied to the adhesive side of the base layer to sandwich the dam patches between the base layer and the cover layer. Individual base units are cut into the base layer, with one of the dam patches positioned within each of the base units. Apertures are cut in the areas of the cover layer overlying the dam patches to access a portion of the foil surface of each of the dam patches. The offal portion of the base layer is removed from the cover layer, forming fabricated base assemblies for the compresses, which are conveniently carried together on the cover layer for final assembly. The dam patch cutting and applying steps may include roller die cutting the web of imperforate material, separating the dam patches from the offal portion by a vacuum operated applicator drum, and pressing the cut dam patches into contact with the adhesive side of the base layer. For final assembly of the compresses, a medicine-filled pad is positioned on each of the dam patches, and an imperforate, removable outer sheet is applied over each of the medicine-filled pads to form sealed reservoirs in which the medicine-filled pads are retained.