70-200mm 2.8 IS II Low Light Autofocus Performance

I just upgraded from a 70-200 f4 IS to the 2.8 IS II and have a question about the 2.8 II's performance while I still have the 2 lenses together. In low light indoors, the 2.8 will sort of "double tap" the focus, if it's not already close to focus, while my f4 lens does not do this in the same situation. The f4 will normally hit the focus in one attempt. The 2.8 will focus to about 95% focus and then immediately re-focus to nail it. The 2.8 also seems more prone to hunting on a low contrast subject than my slower f4 lens, sometimes reusing to focus at all. Does the doube tap focus sound like normal behavior? or does it indicate that the lens is mis-focusing and then correcting itself? This seems to only be an issue in low light situations.

Thanks
Roqdawg

I think it's just getting focus by using the low-precision AF point first (f/5.6?) and then getting more accurate focus by using the high-precision AF point second (f/2.8).

Your camera can't take advantange of this high precision AF point with your 70-200mm f/4, since it doesn't go down to f/2.8.

I don't know about the extra hunting of the f/2.8 over the f/4 lens that you've indicated though.