S.C.
We overpaid for our house in 2001 and didn't realize that the DCAD folks would appraise our property at that amount. I tried to fight it, but they said that if we thought the house was worth that, then we couldn't win. Try again next year...
So I did. I've successfully fought the increase every year except one (when they didn't send me a notice). Here's what you need to do:
1) Check recent sales in your neighborhood. Talk to a realtor to pull those numbers. You should get last year's sales (2006) especially since that's when they made the appraisal on your home. But still get 2007 just as extra info. Are home sales comparable to what your home was appraised for?
2) Check the DCAD site for other homes on your street or in your neighborhood that are comparable in size and condition. Did DCAD appraise your home fairly? If your appraisal is higher per square foot, you can make a case for it. Keep in mind that smaller homes usually have a higher price per square foot.
3) Look around your house - do you have lots of repairs to do? If so, take photos, get estimates. You might be able to get the condition lowered so the appraisal drops. I had lots of water damage, so one year I was able to get the amount dropped with a condition change.
I suggest getting all you info together, then doing the informal hearing (show up at the DCAD office early in the morning) and speak with one of the employees. They will either make the adjustment or tell you why they won't. Then if you need more info, you can gather it before the formal hearing if you choose to do it.
Good luck! It's a bit of work and sort of a pain, but we're still below the amount we were initially appraised for, and I know my house is worth more.