Fingers!
Distracted as we are by the challenges of making our lips vibrate, brass players often neglect finger dexterity. You must have as much technique with your three fingers as a pianist has with 10.
Pushing or releasing a valve changes the length of the instrument by channeling air through the valve slides. The seven valve combinations correlate to the seven positions on the trombone slide. Missed notes commonly result from fingers that move too slowly or the player not being prepared for the sensation of blowing through a longer or shorter tube.
Your fingers must move as fast as possible, regardless of the speed of the notes, and your tongue must be coordinated exactly. Otherwise, the definition of your attacks will suffer, and you may be thrown off your note by the changing tube length. Snap your fingers up and down!
Develop finger dexterity by fingering scales or patterns during breaks in the practice routine. Listen for a defined click on each valve change. Do not accept sluggish or uncoordinated finger movements. Slow down and pay attention! Keeping track of what note you are playing—without hearing the sound—forces you to think.
An additional benefit of these finger exercises is the insertion of additional rest time into the practice session; most players don’t rest enough. Keeping your brain active through the periods of rest will enhance the effectiveness of the entire practice session.
Use the snap of your fingers as a mental focus point: At the piano, play two notes a fourth apart, for example, C to F. Move your fingers as crisply as possible. Now go to your horn and slur the same two notes. Imagine that the pitch change comes solely from the fingers as it does on the piano. Let air and embouchure adjustments happen subconsciously; focus on the precise movement of the fingers. You may be surprised by the way the notes jump out of the horn when your fingers snap to it!