I recently purchased a 99 accord v6 coupe and noticed when I gradually accelerate, as in normal city driving, the car shifts very quickly from 2nd to 3rd. 1st gear would go over 3k, then 2nd gear would come in... but not a half second later 3rd would engage. When I drive it briskly from standing position, it shifts about right.

Is this normal?

 

Worry about it when it won't engage 3rd at all.

You will learn eventually that you can control the transmission very easily, precisely and accurately with the throttle.

I never let 1st go about 3k unless I'm in a big hurry...I usually shift at about 2000-2500.