An insulating cup or container (50) and a method of manufacturing it comprises (first embodiment) providing a sidewall blank (12B) having two sections separated by a fold score (15), and a separate insulating sheet (18) (corrugated, ribbed, embossed, foamed, perforated, etc.) which is adhesively fastened to one of the sections. The blank is folded in half along the fold score, to form a three-layered assembly with the insulating sheet in the middle. To reduce the thickness of the seam, the blank is thinned in the area adjacent a fold score prior to folding. The assembly is wrapped around a mandrel to bring the outer edges together at a side seam (22S) to form a sidewall 12. The side seam is sealed, the bottom is added, and the rim is formed. In a second embodiment, the insulating layer can be a coating on one or both of the sections of the two-section starting blank. In a third embodiment, the insulating section (40) is integral with, and extends from, one edge of the starting blank. It is folded over first to form the middle layer of the wrappable assembly. The width of the seam is reduced while being reinforced at the top by using edge tabs, thereby providing a rounder cup and one which is less susceptible to top leakage due to an unsealed top curl. One tab extends at the fold line from the top edge of one section, which is shorter, to the top edge of the adjacent and higher section. A second tab extends out from the top of the side edge of the higher section so that it overlaps and seals the other tab when the cup is formed.