Tempted by the recent offer of an Italian home for just over a $1? Well, you might want to hold out for a better deal. Now one town in the country is offering foreigners $10,000 to move there. Another says it will even pay newcomers more than $1,000 per child to make babies.

The deals may seem too good to be true for many who dream of escaping the rat race for the idyll of a rustic Italian village. For the destinations involved, they represent a last-ditch battle to save the souls of their dying communities.