This is my normal position for the left hand. Two fingers above and two below the third valve slide.
My right hand is shown with the little finger floating, however, I play a LOT of plunger work in the band and it is more normal for me to have the pinky in the finger hook.
My right thumb, like Christine's sometimes rests right under the leadpipe, at other times I have it around the valve casing.
2nd picture is the pinky in the hook.
-cw-