Quote Originally Posted by pcaravel
No but I think there should be a way to keep a newly conquered city under control without killing everybody or demolishing most of the buildings!
Extermination is normally the required option when taking a city. Early in the campaign you might get away with more lenient choices, perhaps. The restless sleeper trait is of no real significance; you do what you have to do, and live with the consequences. As NeoSpartan said, the residual population will still be pretty large - I think extermination kills 75%, which leaves a city large enough to be troublesome still if the original population was in the top size category.

Regarding the buildings, read Marcus's post more carefully: "Tear them down or upgrade them and the cultural penalties will decrease." This will take decades, but what do you expect, really? It is a pity though that cities captured at maximum size (Carthage, say) will always have that 30% culture penalty from the palace building being wrong culture. Note also that it's usually possible to stabilize a city at zero growth well below it's pre-sack population (I have Carthage and Alexandria at 18k in my game). Destroy the medical buildings and especially any of those estate buildings which add growth and decrease law. Then build a colonia (-1% growth, +10 law) relatively early, say a couple of years after capture. Try to make sure the governor isn't one of those philosopher-farmer growth maniacs, too.

Regarding the original post, in my experience EB cities have a "floor" of unrest in the 25-50% range. Some governors make it better, some make it worse (the happy/unhappy people traits), but there's nothing you can do about it. It's worth keeping a spy in town just in case an enemy spy is making matters worse, though.