In the late 1960s and early 1970s, Texas International was losing a lot of money. It was a stodgy airline that, like Allegheny and the other Local Service airlines, was perceived as a "puddle jumper" (although it did operate DC9s to places like Roswell, New Mexico and Hot Springs, Arkansas.
As was mentioned earlier, deregulation coincided with the Texas oil boom in the late 1970s and Texas International started doing very well. With the government's permission, it dropped service to small cities like Lufkin and Big Spring. Free to set its own fares, it converted its aircraft to all Y-class and started charging bargain basement-style fares. It built its route network around IAH and DFW (after the Continental merger, the DFW hub was abandoned and most of its Terminal 2E gates were given to American.)
I have a Texas International timetable from 1973 and one from 1980, and the difference is astounding. Where in 1973 TI serves nine states (TX, LA, AR, NM, TN, MS, CO, CA, UT) and dozens of tiny cities (Clovis, New Mexico; Pine Bluff, Arkansas; Longview, Texas), in 1980 it is a real powerhouse with a strong east-west network across the southern states. Texas International was also one of the first airlines to tap into the potential of Baltimore/Washington International Airport with service from IAH and DFW. By 1980 it was serving BWI, LAX, SLC, TPA, MIA, and a slew of Mexican resort destinations.
What I find interesting is that it was actually Texas International that bought Continental, instead of the other way around. It was decided by Frank Lorenzo that the Continental name was more recognizable nationwide, and thus it was retained. At the time the merger was a great idea, as CO and TI overlapped on many routes (Continental had a sizeable Texas network throughout the 1970s), and a merger helped it solidify its flank against the failing Braniff and the booming Southwest.
If you haven't figured it out, in addition to being an aviation nut in general, I'm also a Texas airline history buff.