kievins

I play Eb tuba. Before my range was from Bb1 to D4 (if you were lucky), now it's from G1 to E4. Apparantly, since I already have a good low and middle register (I don't know if that is how you spell it), my high register will come. I just wish I could get to that bit sooner.

Basically, amend fingering. Do you really need to use a 1 and 2? Can you cut corners with just a three? Or on a really difficult note, I discovered that on D4, it was easier to play with 1 and 2, instead of just 2, which I normally did.
Also, the harder the note is to play, the more air you need. This kinda sounds obvious, but it's amazing how much you really need. You may need an entire lungful of air for one note, so you'd be kinda screwed if that was a really long note...
The tendancy with difficult notes is to either tense unnecessary muscles (such as shoulders), or to press the mouth closer to the mouthpiece, or both (in my case both). Don't. All the energy should be going into blowing, and getting lots of air out of the lungs very quickly. This is why breathing excercises help.
I don't know if that helped.