I've found that if you half press the shutter button and wait for the AF light to and point to flash, it takes 3 sec or more. However, if I just press the shutter button down all the way, it focuses in about 1 second or less and fires with perfectly sharp focus.
It does this regardless of AF-Assist or not. So, if you are waiting for the AF- Assist to stop flashing to take the image, just press and hold the shutter button. It fires as soon as focus is reached rather than delaying another 2-3 seconds before the focus points light up.