Thanks to the help of the guys at the #radeonhd channel on Freenode.net, I could quickly find out how to make DRI (and thus, EXA) work with my laptop's onboard graphics... thingy... I'll let lspci speak for itself; it's much easier that way:
shadowm@bluecore:~$ lspci 00:00.0 Host bridge: Advanced Micro Devices [AMD] RS780 Host Bridge [...] 01:05.0 VGA compatible controller: ATI Technologies Inc RS780M/RS780MN [Radeon HD 3200 Graphics] [...]
Let's not forget that this is my current (it was new on December) laptop, not the old, broken lappy, and I'm running Debian stable.
The thing is, with their help I installed a newer-than-Debian (or actually, newer-than-the-kernel-that-is-newer-than-Debian's) radeon drm module, and also solved a little mistake that made X lock up after resuming from suspend-to-disk with DRI and EXA enabled. Now I can enjoy some real 2D acceleration at last!
Although it seems, judging from the git repository's logs, that the official EXA and XRender acceleration support for this chipset is pretty recent, it is very stable compared to a certain other driver for another onboard chipset which I won't mention here. I could even enable KWin's composition manager (kompmgr)!
I have not tried the other big composition/window managers (e.g. compiz), nor intend to, as they require a hardware OpenGL interface which is not available yet for this chipset, and since they are labeled "window managers", I'm guessing that I'll definitively lose the KWin look-and-feel that kompmgr doesn't intend to replace).
Nonetheless, my very limited candy set-up has an incredibly low CPU overhead (either that or the radeonhd driver is f***ing awesome), and I can even let it enabled while in powersave mode, and no matter what I do, I don't see any impact in the other program's performance. I couldn't say the same thing about radeonhd before getting EXA.
One really odd thing I noticed, though, is that kompmgr doesn't seem to want to have anything to do with translucency and pop-up menus. Side-effect, it is KDE (Qt3?) itself who must provide and option for that in the Control Center -> Styles page. But even if I tell it to use XRender acceleration, something doesn't fit - and it is that the changes going on windows below a pop up menu are not seen, e.g. the pop up menu rendering is completely static. This unlike regular translucent windows. I don't know what benefits this design decision may bring, but it's KDE 3.5.10 anyway, and KDE 4 users would laugh at me for my obsession with not switching to 4.x.
Note that I am aware that 4.2.x has fixed a lot of the stunningly awful usability and configurability regressions seen in earlier 4.x versions. But I am still pondering why all Qt 4 widget engines are pretty slow, compared to Qt 3 - so, until I get an answer of the kind "it's just you" or "can be solved" or "has been solved already", I'll not consider switching to KDE 4 an option.