We discuss the effect of a gravitational field on the first-order wetting transition of a liquid layer on a horizontal surface. Gravity limits the thickness of the wetting layer and leads to a smooth first-order transition line Delta mu(w)(T, g) in the wetting phase diagram of chemical potential difference from bulk coexistence, Delta mu = mu - mu(c), temperature T, and gravitational acceleration g, Consequences for the interpretation of wetting experiments are pointed out.