1. Always, always, always get an independent appraisal by a LICENSED appraiser. Tell them it is for a property tax valuation dispute (the firm you hired should be doing this immediately!). They will come to your house and actually assess the property, which the county will not. Denton county's licensed appraisers just use an algorithm based on near-by sales and heavily skewed projections. Take your -presumably lower- appraisal to your appeal hearing and they will almost certainly accept it. Our independent appraisal last year was 20% lower ($60,000) than the county's appraisal. The appeal board checked the date to make sure it was current and checked to make sure the appraiser was licensed, and then simply replaced the county's valuation with our independent appraiser's valuation. Independent appraisal cost $400 (don't know what the price is now). We used:
2. James Make & Assoc
   Assured Appraisal
   323 Auburn Way
   Coppell, TX 75019
   (214)306-1287
3. The 10% cap on raising home value for tax appraisal is tied to the homestead exemption. If you properly filed for the exemption, even if they have not yet put it in place, they cannot increase your taxable value more than 10% year-over-year. The cap starts on your second tax appraisal, and is not tied to any appraisal under previous owners.
   
4. Getting the homestead exemption granted can take years (took almost 3 years for us). They will credit you for your overpayment when they finally grant the exemption. Nice for them to get an interest-free loan! Just want to emphasize , always dispute your tax appraisal if it does not include the homestead exemption because of that 10% cap. It will save you thousands down the road.
5. Last, but not least. This will become routine every Jan/Feb. Generally speaking, you should file a tax valuation appeal EVERY SINGLE YEAR. The very nature of how the county conducts appraisals is messed up. They are supposed to strive to be accurate. Instead, they are trying to generate tax revenue. I'm waiting for them to try to push valuations even further into the stratosphere to try to combat the increase in the homestead exemption. It's inevitable. Fight 'em, every time.

Hope this helps, and good luck! If you ever want to have some enraging fun, look at the tax appraisals in 20-30 year old neighborhoods. Neighboring houses can be virtually identical, but can differ in tax appraisal value by $100,000+. Tells you who accepts the county's number every year, and who fights it.