Sulfur emissions from liquid sulfur are reduced, or even entirely avoided by degassing the liquid sulfur at pressure in an out-of-pit vessel and by sweeping the rundown pit (or vessel) with a sweep gas that is non-poisonous for a hydrogenation catalyst. Acid gases from degassing are fed at pressure to the Claus unit, while sweep gases are fed to the tail gas treatment unit to substantially recycle the acid gases to extinction. In preferred plants and methods, motive fluids and booster eductors or compressors are not needed, and incineration of the acid gases can be avoided.