The Government should give prize money to people to get themselves sterilized. No restrictions -- you can use the money to settle your bill at the crack dealer, or you can invest it. Put the person on a blacklist that they can't get a reversal for 5 years (this weeds out the idiots who will just blow the prize money.) If you take the money, insurers are forbidden from covering a reversal procedure, although you are free to pay cash. One time deal -- you can't do it twice.
Realistically, only really, really poor people or desperate people or financial idiots would see this as a good deal, and frankly we really don't need their genes floating around anyway.
Cost analysis: Calculate the average amount of money in government services saved if some poor person were to become neutered and/or spayed. Discount that by 50% and offer that as the payoff to poor person to get snipped.
I'd offer it to the everyone, though because even though some non-poor person might statistically output more tax donors than recipients, he doesn't need to be passing his genes along anyway.
Win-win.