[Linux][Solved] Framerate drop with AMD/ATI graphics card

I ran into an issue with an AMD/ATI graphics card on Linux - both the editor and the build. I managed to solve it, so I'm posting it here in case anyone else has a similar issue.

My graphics card is an AMD/AMI Oland (HD Radeon 6800 series). I had the recommended X.Org X Server driver installed (version 1:7.3.0-1ubuntu3.1), and my framerate dropped to less than 50 FPS on an empty project, while running in the Editor and with Maximize on Play unchecked. With Maximize on Play toggled, this dropped to 30 or less. Add anything to the scene - even a static, untextured object with no colliders - and it dropped to 15 or even 10. This occurred in the Linux build as well, but when I tested a Windows build on a separate machine it worked perfectly fine.

I'm running Linux Mint 17.2, which kept telling me that it was running in software rendering mode upon startup. When looking for a fix for that, I found this thread elsewhere. I switched the driver to use fglrx-updates (version 2:15.200-0ubuntu0.5), but didn't run the aticonfig command, and then restarted my computer. That fixed the issue - I'm now getting up to 1000 FPS on an empty scene, and 80-90 on the scene where I first noticed it.