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.