A lid for a beverage cup includes: (a) a radial collar configured to engage with a rim of a drinking cup mouth, having an inner radial surface and an outer radial surface; (b) an outer reservoir wall extending axially upward from the outer surface of the radial collar and enclosing a reservoir chamber above the radial collar, and including an upper rim; (c) a reservoir floor extending radially inward from an upper end of the inner surface of the radial collar and substantially closing the reservoir chamber from below the reservoir floor, the floor including a fluid path opening providing at least part of a fluid path extending upward through the reservoir chamber, the fluid path opening being positioned along a first diametrical line extending through the reservoir chamber; (d) an inner wall separating the fluid path from the reservoir chamber substantially in the shape of an upside-down funnel extending upward from the floor, having a minor diameter extending above a vertical level of the upper rim of the outer reservoir wall to form a spout; and (e) a cap connected to the upper rim of the outer wall with a first living hinge and including a first segment with a hole adapted to receive the spout.