. . . when mobsters want to avoid even the hint of an appearance of impropriety. From the latest (compulsively readable) Victoria Gotti excerpt in the New York Post:

John was to be inducted into the family, La Cosa Nostra, or whatever the media and the government calls it. We referred to it as the life.
He was handed a picture to hold in the palm of his hands — a picture of a saint — that had received a drop of blood from his father’s finger, pricked by a knife. The picture was burned while an oath of loyalty was recited. John pledged that he would hope to burn like the picture if he were ever to betray La Cosa Nostra.
My father was not in attendance, to avoid an overtone of nepotism to the proceedings and to avoid possible bad luck.