2.0.2.A.0.24 [mini/mini pro] can now be rooted
1: get SuperOneClick from its original thread
if you don't already have it. Latest version is 1.5.5, but most versions seem to work fine.
2: Delete the "rageagainstthecage" file (no filename extension).
3: get psneuter.zip from the Xperia X8 Android Development forum thread
4: Unzip it. Rename "psneuter" to "rageagainstthecage" (no filename extension), and move it to your SuperOneClick folder, to replace the rageagainstthecage file you deleted in step 2.
5: run SuperOneClick. Mine rooted without looping.
6: reboot your phone. Test your shiny new root!
Remember to put your phone in debugging mode, etc. Someone in the X8 thread claims that X10 Mini can be rooted via this method; I don't have a Mini so I don't know for sure. But I've got a Mini Pro and it just worked.
The file you need in Step 3 is "psneuter", not "psneuter.c". psneuter.c is the source file for psneuter. You can ignore it.
says that if you have problems with Titanium Backup (even after step 6!), uninstall it, reboot, and reinstall Titanium. This appears to have worked for several users.
says that s/he had to install drivers from the Sony Ericsson PC Companion for SuperOneClick to move past "waiting for device". I had PC Companion already installed when I did mine, so I don't know whether the process works without PC Companion... if you don't have PC Companion, you can get it here
The latest version of SuperOneClick now includes psneuter; you no longer need to follow the steps above. Just use SuperOneClick!