It was in the third week of the Iraq war, as U.S. troops barreled toward Baghdad, that Sgt. 1st Class Paul Smith's band of combat engineers found themselves on the wrong end of 10-to-1 odds. In a walled courtyard not far from Baghdad's airport, Smith and his 15 lightly armed soldiers were trying to hold off 100 Special Republican Guard fighters wielding rocket-propelled grenades, mortars and AK-47 assault rifles. When wounds downed the U.S. crew of the armored vehicle bearing the Americans' sole heavy machine gun, Smith scrambled into the breach. In the gunner's hatch of that personnel carrier, with...