UPDATE:

This is not a request for support of my specific issue. Details of that issue are here: How to recover from bad upgrade to 13.04 (Unity very slow) . I have "solved" that issue, for the time being anyway, by loading alternative lighter weight desktops.
This question was opened specifically to question the meaning of the documentation at https://help.ubuntu.com/community/RadeonDriver .

END OF UPDATE

There it is, in Black and White:

https://help.ubuntu.com/community/RadeonDriver

Fully Supported All these Radeon(HD) cards and derivatives have good 3D acceleration support. This is not an exhaustive list: ... RV610/RV630 Radeon HD 2400/2600/2700/4200/4225/4250

Yet in my case (the HD2400) this proves to be manifestly untrue, at least if "Fully Supported" means sufficient to run Unity in Ubuntu 13.04.

It runs all the applications I can launch under Unity, but Unity itself is unbearably slow. It's quite striking really. Click on the "Dash" - go get a cup of coffee. Type a key in the Unity search box, wait five seconds for it to appear. Type Alt-tab and wait five seconds for the screen to finish painting. None of these issues appear outside of Unity components. As you all know, there are complaints about slow performance all over the Internet about Unity.

Shouldn't this page somehow address this issue? Especially if "fully supported" doesn't mean sufficiently to run the default modern Ubuntu release.

What does "fully supported" mean?