Further from Paul:
1Cr 11:3 But I want you to understand that Christ is the head of every man, and the man is the head of a woman, and God is the head of Christ.
1Cr 11:4 Every man who has {something} on his head while praying or prophesying disgraces his head.
1Cr 11:5 But every woman who has her head uncovered while praying or prophesying disgraces her head, for she is one and the same as the woman whose head is shaved.
1Cr 11:6 For if a woman does not cover her head, let her also have her hair cut off; but if it is disgraceful for a woman to have her hair cut off or her head shaved, let her cover her head.
1Cr 11:7 For a man ought not to have his head covered, since he is the image and glory of God; but the woman is the glory of man.
1Cr 11:4 Every man who has {something} on his head while praying or prophesying disgraces his head.
Here's a description of Syriac Orthodox vestments that include head coverings for the priest: http://sor.cua.edu/Vestments/
"The priest then puts on the phiro (lit. 'fruit'), a small black cap which the priest must wear during all public prayers. It consists of seven sections which indicate the full priesthood of the celebrant. Bishops including the Patriarch wear it under the Eskimo."
Are Syriac Orthodox priests bringing disgrace upon themselves? After all, they're required to lead prayers with their heads covered...