Eastern Rite Priests, if they are ordained in North America are technically not allowed to be married at the time of their ordination. This is the result of a Papal decree dating from the early 20th or late 19th century.
This rule has been broken a couple of times in the past few years by Eastern Rite Bishops, but it is still in place.
Unless I'm mistaken, the decree was issued at the request of the U.S. Bishops, through the premier diocese of Baltimore. If the pope would revoke the decree, it would go a long way to resolving the problem. JMO.