anarres
anarchist revolutionary
I've seen a few people talk about flips from newly 'aquired' cities, and thought it may be worth stating how I deal with them. Some people may consider this exploitative, but please bear in mind that this is how I play the game. How you do so is up to you. 
On deciding to take enemy cities there is only important question you need to ask yourself:
Can I take the civ out entirely within a reasonable number of turns?
If the answer is yes, then you are in good shape to take all their cities and keep them (although I often raze a few just for the workers, or because of poor map placement).
If the answer is no, you can still follow this strat, but you will have to starve all your cities to size 1 to be on the safe side, and you should raze all cities bordering the other civ. Every tile in your 21 city tiles under their cultural boundries counts against you, and unless you are also going to take those cities soon, you will face a much higher chance of flips.
So, here's what I do:
- Take city, and garrison as many military units in it as possible. I believe that it is impossible for a city to flip back the turn you take it, so your units should be safe. Note that this is just from observation. I have had no flips on turn 1, but many many flips on turn 2.
- On the next turn, move all of your troops out of the city. Even if you haven't quelled any resistors, there is a chane of flip, and if does you lose your troops. Make sure to leave at least 1 or 2 offensive units next to the city.
- If you are not going to take out the enemy civ in it's entirety soon, you must starve the city to size 1 to reduce the chance of flipping. Set all citizens to entertainers, ignore the resistors for now. Each turn, set all the citizens to entertainers again, until you are size 1, or you are down to just resistors (and 1 citizen that won't starve because of the worked city tile giving 2 food). At this point you must move as many units in to the city as possible for 1 turn only (again), and try to quell some more resistors. Next turn move them out and repeat the process until the city is size 1. When the city is size 1 garrison a few units in it, until the enemy civ is completely destroyed.
- If you are going to take the civ out soon, make sure never to leave units in it (apart from the first turn)
- When the city flips (and most size 12 cities will flip, especially when you are in 'awe' of their culture), just retake the city with your offensive units placed outside. Note that if the city flips it will get one defender, the best it can build in that city (so rifleman if in industrial age, pikeman if not there yet and iron connected to city, etc.). You should decide exacly how many offensive units to leave by the city based on the defender it will get if it flips. Not having the required firepower nearby can be very frustrating!
That's about it, although there are some more things I normally take in to account:
- If there are some far-flung cities from the civ you are capturing, I often take nearly all their cities near me, make peace (getting all the far away cities), then re-declare war and finish them off. This will give you a rep hit, and many people wouldn't use this strat out of honour, but that is your preference. Even a far-flung capital and flip a conqured big city you think is safe.
- Don't worry about flips, just make sure not to lose your units...
- If you care about Reputation, don't make peace until all the captured cities are reduced to size 1. If one flips you will have to declare war again to take it, and if you don't the 'flipped' city will really annoy you.
- Once the enemy is destroyed, all the big cities with lots of resistors in will soon calm down. There is no chance of flips now, but you must remember to quell the resistance still. If you miss a city and forget to put troops in it you will always have resistors.

On deciding to take enemy cities there is only important question you need to ask yourself:
Can I take the civ out entirely within a reasonable number of turns?
If the answer is yes, then you are in good shape to take all their cities and keep them (although I often raze a few just for the workers, or because of poor map placement).
If the answer is no, you can still follow this strat, but you will have to starve all your cities to size 1 to be on the safe side, and you should raze all cities bordering the other civ. Every tile in your 21 city tiles under their cultural boundries counts against you, and unless you are also going to take those cities soon, you will face a much higher chance of flips.
So, here's what I do:
- Take city, and garrison as many military units in it as possible. I believe that it is impossible for a city to flip back the turn you take it, so your units should be safe. Note that this is just from observation. I have had no flips on turn 1, but many many flips on turn 2.
- On the next turn, move all of your troops out of the city. Even if you haven't quelled any resistors, there is a chane of flip, and if does you lose your troops. Make sure to leave at least 1 or 2 offensive units next to the city.
- If you are not going to take out the enemy civ in it's entirety soon, you must starve the city to size 1 to reduce the chance of flipping. Set all citizens to entertainers, ignore the resistors for now. Each turn, set all the citizens to entertainers again, until you are size 1, or you are down to just resistors (and 1 citizen that won't starve because of the worked city tile giving 2 food). At this point you must move as many units in to the city as possible for 1 turn only (again), and try to quell some more resistors. Next turn move them out and repeat the process until the city is size 1. When the city is size 1 garrison a few units in it, until the enemy civ is completely destroyed.
- If you are going to take the civ out soon, make sure never to leave units in it (apart from the first turn)
- When the city flips (and most size 12 cities will flip, especially when you are in 'awe' of their culture), just retake the city with your offensive units placed outside. Note that if the city flips it will get one defender, the best it can build in that city (so rifleman if in industrial age, pikeman if not there yet and iron connected to city, etc.). You should decide exacly how many offensive units to leave by the city based on the defender it will get if it flips. Not having the required firepower nearby can be very frustrating!
That's about it, although there are some more things I normally take in to account:
- If there are some far-flung cities from the civ you are capturing, I often take nearly all their cities near me, make peace (getting all the far away cities), then re-declare war and finish them off. This will give you a rep hit, and many people wouldn't use this strat out of honour, but that is your preference. Even a far-flung capital and flip a conqured big city you think is safe.
- Don't worry about flips, just make sure not to lose your units...
- If you care about Reputation, don't make peace until all the captured cities are reduced to size 1. If one flips you will have to declare war again to take it, and if you don't the 'flipped' city will really annoy you.
- Once the enemy is destroyed, all the big cities with lots of resistors in will soon calm down. There is no chance of flips now, but you must remember to quell the resistance still. If you miss a city and forget to put troops in it you will always have resistors.