Lyrical Playing, part I
You want your airsream in the lyrical pieces to be as energized and steady as if you were playing fast. It is common in lyrical pieces to play with lack of direction and intensity in an effort to play prettily, but avoid this temptation. Think about accelerating your air all the way to the end of a phrase. An exercise that helps is to just play your leadpipe (take out the tuning slide). You should be playing a steady, unwavering long tone while fingering something technical like a Clarke study and imagining the notes you are fingering (it is quite difficult at first to avoid lipping in the direction of what you are fingering). Take the intensity from that long tone and apply it to lyrical pieces. As an added bonus, this exercise is also great for alleviating excess movement between notes (which is a common culprit for tension, pinched sound, lack of flexibility, and poor endurance). Take any piece that you are working on and play it on the leadpipe with all the correct fingering and articulation, but hold the pitch steady. Aim for a big, lively, open sound.