I bought a vocal course a while back which included some excellent vocal exercises. After a few weeks my vocals were much better and I noticed a marked improvement on my diaphragm strength. It also managed to extend my normal vocal upper range by 2 tones and my falsetto range by around 5 tones.
Here's the basic routine:
For each of the exercises, start at the lowest comfortable note you can sing. Do NOT strain at any point as you go up the scales, and let your voice naturally go to falsetto (even if this is a lot lower than you'd normally switch to falsetto).
The scales should go up and down 5 notes at a time, e.g. F, G, A, Bb, C then back down Bb, A, G, F. Then go on to G, A, B, C, D and back down C, B, A, G, etc. Each up/down scale should be done in one breath without a pause or break. Go up the scales until it's no longer comfortable - remember not to force higher notes during the exercises. With all the exercises, try to relax and let it resonate around your head, especially around your sinuses.
Exercise 1: Humming an "N" sound.
Exercise 2: Humming an "M" sound.
Exercise 3: Rolling "R"s (like your Scottish)
Exercise 4: B's like blowing a raspberry - you may find it easier to press your thumb and fore-finger either side of your lips else you'll end up spitting everywhere.
Do these exercises 2-3 times, and notice the difference when you sing afterwards.
M.