No; don't bring it up with a jerk.
Do it like this---smartly, without jerk.

No; that's not right, either.

Hold your hand horizontally when it touches your hat-brim.
Hold it the way I am doing.

Don't be in a hurry to let hand fall, either.

When saluting an officer, keep the hand at the hat-brim until he has returned the salute, or you've passed him.
There, you have it right now, Rindle.