A disposable spittoon cover for a paper cup or the like includes a conical tunnel with an entry hole near or at an apex of the tunnel, and an integral, resilient flap covering the entry hole. The flap may be formed at a slight angle to the tunnel walls, in the range of about 5° to 20°. The disposable cover may further include two or more concentric grooves configured for fitting snugly to rims of disposable cups, with each of the grooves configured to fit to a cup of different diameter. The grooves may be separated and spaced apart from one another in a direct transverse to a plane defined by any one of the circular grooves (e.g., a “vertical” direction), by one or more interposed annular ring walls.
