Dear Bob, The weight of halakhic opinion is that the principle צער בעלי חיים, which prohibits causing unnecessary pain to non-human life, refers only to pain during life-time, and not to death itself. Painless death may, under ordinary circumstances, be proscribed on the grounds of בל תשחית – i.e., vandalism or wanton destruction – rather than pain. These circumstances are not present, however, in the situation you described to me, namely, an old dog which is sick to the point of debilitation.I have found no reference in the literature to the analogue, in animal life, of "mercy killing." However, as I explained above, as long as the killing of the animal is not an act of wanton destruction, and is painless, there is no prohibition in doing away with it.(For your information, the major source dealing with this issue is Rabbi Ezekiel Landau of Prague, in his Noda B’Yehudah.)Finally—my congratulations on having the good sense and intuition to pose a she’elah on an issue so many others never assume comes in the purview of Halakhah.Cordially,RABBI NORMAN LAMM