CUP LID WITH ROLL AND SPILL LIMITING RIM

A beverage container lid includes a round rim and a flange extending beyond the rim at least proximal to a spout, such that the container, when tipped over with the spout oriented downward, will gravitationally roll until a height of the container's center of mass reaches any of a plurality of local minima. The lid can be configured such that rolling through an angle of no less than 30 degree and/or no more than 90 degrees is required. In some embodiments the flange extends beyond the rim only proximal to the spout, such that the rim contacts an underlying table over a continuous angular range beyond the flange. In other embodiments, the flange extends beyond the rim everywhere, and has a plurality of maximum radii with a plurality of minimum radii interspersed therebetween. In some of these embodiments the flange includes at least one flat, straight line segment.