From the Harrelson Wesite... I adopted this hand position and it makes the horn more stable when adjusting the tuning. See below:
Trumpet Holding Ergonomics
1. The weight of the trumpet should be held in your left hand only.
2. Holding your trumpet with 2 or more fingers under 3rd slide is more stable & reduces fatigue. I recommend putting index/middle finger through the 3rd slide ring. Your trumpet bell should NEVER rest on your index finger. This is sometimes not possible if your trumpet has been designed to place all fingers above the 3rd slide. In this case, the 3rd slide finger ring may need to be re-positioned closer to the 3rd valve casing.
3. Brace your left elbow against the side of your rib cage. This position improves resonance and helps prevent back fatigue.
4. Use the right hand pinky hook/ring only when playing with a plunger mute or when your left hand must be removed from the trumpet.