In an embodiment, a method of hydrogenating a highly unsaturated hydrocarbon to an unsaturated hydrocarbon includes contacting the highly unsaturated hydrocarbon with a catalyst in the presence of hydrogen. The catalyst comprises palladium and an inorganic support having a surface area of from about 4.5 to about 20 m.sup.2/g, or alternatively 5 to 14.5 m.sup.2/g. The inorganic support may comprise .alpha.-alumina treated with a fluoride source. The palladium may be primarily disposed near the surface of the support. In addition, the catalyst may comprise silver distributed throughout the support. In another embodiment, a method of making the foregoing selective hydrogenation catalyst includes contacting a fluorine-containing compound with an inorganic support, heating the support, and adding palladium to the inorganic support. After adding palladium to the support, the support can then be heated again, followed by adding silver to and then heating the support once again.