Abstract: A unitary disposable beverage container sleeve that can also be used as a coaster and that can be comprised of (optionally recyclable) cardstock for economically imprinting with advertising logos or slogans. The upper body vertical rectangular edges are connected to form sides of the sleeve and a gusset extends across the diameter at the lower edge to form the base of the sleeve. The gusset has a hinge that opens and closes the sleeve. Arched grooves positioned at that lower edge above the gusset where the gusset attaches to opposing sides of the sleeve allows flex in the sleeve and affords a level base.

Abstract: A disposable beverage container sleeve has a substantially rectangular upper body and a gusset. A resiliently flexible lip is disposed along the top edge of the upper body. In the assembled state, the assembled sleeve is now easily opened by applying the index finger to one edge and the thumb to the other edge, then squeezing. As the consumer squeezes the edges towards each other, the resiliently flexible lip bends, causing the rest of the upper body of the sleeve to open. As the upper body of the sleeve opens, the gusset unfolds by the stretching, forming a cup in which to insert the beverage container. The lip, wanting to relax to its natural uncurved state, urges against the beverage container. This partially reduces the duties of the upper body in providing frictional adherence to the beverage container.