Just as the title states...I have a child with an ex with whom I owe child support to in the amount of $1219/month (yes...for one friggin child). I'm currently making $102k~ annually while my wife makes $40k. My ex makes a measly $21k/year. She obviously refuses to get a better job because she knows what she can get from me. My current wife and I are expecting a child in Jan 2014 and couldn't be any happier considering we've been trying for 9 months. She plans on leaving her job for a year to be with the baby, but that leaves our family income to me. I believe we'll be ok, but a slight reduction in my current court ordered support would be beneficial. Do I have a chance at getting my support lowered?

TL;DR - New baby on the way, do I have a chance at reducing child support payments with the ex?