What does the abbreviation "S. D. N. D.", common in papal bulls of the 16th century at least, stand for?

Here's my first guess:

". . . Sancti(ssimi) Domini Nostri, Domini [Pii] . . ." (where the second and largely superfluous occurrence of "Domini" is sometimes dropped, as in the abbreviation "S. D. N.") 

". . . of Our (Most) Holy Lord, the Lord [Pius] . . ."

See, for example, the top of this page in the important 1853 Richter/Schulte edition of the Canones et decreta Concilii Tridentini here, where, however, some additional words intervene, so that what you get, severely abbreviated further on down as "S. D. N.", is

". . . the pontificate of Our Most Holy Father in Christ and Lord, the Lord Pius IV, by divine providence Pope . . ."

Cf. these 19th-century translations of the Tridentine bulls of Pius IV (just one in a whole series of bulls that begin in this way).  Cf. also (as some specialists on FICINO reminded me) Cappelli's Dizionario di abbreviature latine ed italine, sv S.D.N.