I tried iconifying IB2.4 just now (from it's own private screen), which it does instantly.
Like you, I noticed that it takes approx 3-4 seconds to re-open the private screen and re-draw the windows. That's on this A4000T/060 and a browser screen of 1024 x 768 (Picasso IV).
It looks like when you iconify IB, it simply keeps the HTML data, but not the rendered page. So when you re-open it, all pages which you previously had open must be re-rendered. Therefore if you have a number of browsers/windows which each have a fair bit of HTML layout work to be done, then IB is going to take even longer to redraw everything.
Don't know how AWeb does it, it probably stores a copy of the rendered page instead.
I never use the iconify feature anyway as I find it more convenient to have IB on it's own private screen, so keeps it from cluttering up any other screens. Switching between screens is of course nearly instant.
