I'm not a master of the game but have played CIV 4 quite a bit and finally found that you need control overcrowding and unhappiness using the following:
1) early in the game when your cities are new and smaller, you usually don't have to worry about these factors. You can focus your production on units, wonders and generally key research buildings. I find research bonus are good to get first and/or religion, which in turn can help research, in order to research the advance tech quicker. Some of the advance techs offer options and building that improve health and happiness.
2) In your city interface there are some buttons near the lower right that control automation of production, reasearch,etc. and that allow you to control growth. The control growth button became my friend As your city reaches a certain population size in relation to health and happiness, I click the button to stop growth until i can build improvements and wonders that will add to health and happiness
3) Once you can increase health and happiness a few points, I click the button to allow growth and increase my population. Of course, the extra citizens can be used on resources to improve production, income and food, or to use as scientists, priests, etc.
4) Again keep an eye on these factors and stop growth temporarily until you can improve things. Some wonders provide unlimited health or happiness in a city if you can build them. Build these in your largest or most productive cities as you can only build one of these wonders
5) Lastly, the slavery civic offers the option to sacrifice citizens to speed up production. Sacrificing citizens serves multiple purposes at the same time, but should be used judiciously and timely. For instance, i sacrifice citizens to speed prod on an important improvement or wonder that will provide a significant benefit to my city or civilization such as research, health or happiness, or indirectly leads to these improvements. Additionally, and most relevant to your question, is that sacrificing a citizen at points when your city is overcrowded, and therefore unhealthy and unhappy, WILL, while increasing unhappiness, improve health and balance unhappiness by virtue of having less citizens. Also, this is good for developing new cities or conquered cities faster. Use this option wisely though because the effect I described can be negated by overuse too soon as the unhappiness will increase to fast in contrast to the gain received in reducing population.
Also, note that while slavery is a civic used generally early in the game, you can switch back to the civic temporarily in later stages in the game if you choose to take use of the sacifice citizen option. Usually though, my cities are highly developed and stable by this point, but in some historical scenarios that top out at less advanced civics this option may still prove prudent
6) Lastly, a city may basically reach a cap in which you want to stop the growth pretty much for good
edit:
one more thing, certain civics provide bonuses in health or happiness based on certain conditions. keep an eye on your civics especially at certain points in the game. some are better for times of war to not only improve unit bonuses but keep cities happy during times of war, especially by the number of fortified units stationed in the city.
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