actually... Once a society starts to gain wealth and some certainty and prospects in their economic future, fertility rates drop rather dramatically...
This is quite obvious if you imagine the condition of much of the poorer sections of the world where survival of a family often depends on the number of hands/feet (children) to tend fire, gather firewood, fetch water, tend animals, ward of robbers... Children are produced for all those things with a mind to high child mortality Just human nature..
Once economic and overal security is improved somewhat along with a reduction in child mortality, then the fertility rates drop rather quickly.
So if you are seriously worried about population get to work on making sure your poor neighbors move up the industrialization latter quickly and get some share the wealth...
General cheap energy is the best way to accomplish this, or at least enable a kick start of the process...
