I finally made the switch from GA to Open Web Analytics. I'm already fairly experienced with PHP, which I considered a point in its favor, but I honestly haven't had to do anything with it other than copying it to a server and configuring a few basic settings.

The tracking code seems very lightweight, and I haven't found it lacking any of the features I was using in GA. I've tried a few, and OWA was the first that met all my criteria (100% free software, open source, actually works).