Havoc appears to be missing the point that birth rates have already dropped significantly across the Western world. The USA has a birth rate of 2.05, which means that they're only just keeping a constant population from generation to generation (though the childhood mortality rate will mean that they're probably not even doing that). Australia and many other countries has a birth rate well below 2.
In order to solve overpopulation, you would have to focus your efforts on the third world. And, frankly, there are a lot of other issues you would have to solve before that. You'd need to educate the population on birth control, you'd need to set up some sort of social security infrastructure so that people are supported in their old age when they only have one or two children. You would essentially need to create a middle class out of nowhere so that families could support themselves without having such a large number of children.
And, frankly, if you managed to acheive all that, you wouldn't need to mandate low birth rates - it would happen on its own.
In case you're interested:
List of countries and their birth rates.