Good timing for your question, David. I am going through the same thing right now so I can give you a rundown of what I have to do here in Colorado - which is pretty involved...
1) Get the VIN certified by the CSP (state patrol).
2) Request a title and lien search, if no record, you're good. If someone is on record as owning the vehicle and still holding title, you need to, as you mentioned, send a registered letter to the last registered owner asking them to
release their interest in the vehicle.
I have actually just found the owner of the car I bought, so I am in the process of having him release his interest - I do have returned cert. letters from his old address in case.
He's about on his 10th address in the past 5 years in 4 different states.
3) If there is a lien on the car, you must have the bank give you a notarized lien release letter. I've done this. As long as nothing is still owed on the car, they'll give you one with no hassle.
4) Establish the retail value through appraisal by a dealer.
5) Purchase a "Surety Bond" for 2 x the [now established] retail value of the vehicle.
6) Submit appropriate paperwork to the state for the issuance of a new title
It's a long list, but has to be done if you want to drive the car - at least here in CO.
Hope it's not this involved in TX, but after these steps are taken here, you are issued a clear title, which is important to me.