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Re: Smiley...The Tuba
For higher register, act like you're blowing on a bowl of soup to cool it off. Do this away from the instrument first. Air should naturally be angled slightly down with this being the case. Additionally, this should bring the corners in and forward instead of back. While doing this, emphasize "tall" lips. Closer to sign language letter E, but a little bit less flat.
Air direction plays a massive role in changing between registers. Brass work the opposite of flute; flatter air means a more relaxed bottom lip and lower pitch, while air that's directed down will result in higher partials sounding. Tongue position can aid in this as well.
Sorry for the stream of consciousness. Hopefully this helps just a little.