I like this one because it suggests a private get together between two people to confer, conspire, or just work out a private agreement. There is also the implication that the conversation is held in confidence. Literally, the words are head to head. In Germany they say unter vier Augen, or under four eyes. The meaning is the same. The Spanish phrase mano a mano, literally, hand-to-hand, has a completely different meaning, suggesting a hand-to-hand, one-on-one fight to the finish.