An insulating cup sleeve has a flat, elongated blank with straight top and bottom edges and end edges, and has a plurality of transverse slits that cut into the blank, spaced apart from each other and cut at least partway across the height of the blank, which slits serve to expand the sleeve around the circumference of the cup when the slits are situated along the upward edge of the sleeve. The transverse slits terminate at a larger area cut-out that disperses the tearing pressure at the end of the slit. The new insulating cup sleeve uses about 13.4% less material and takes up about 19.4% less physical space than the prior art sleeve, thus constituting substantial savings on materials and production cost, as well as on transportation and storage.