Phil Appenzeller, the longtime chief executive officer of Munsch Hardt Kopf & Harr, said his firm increasingly outsources office services such as hospitality, mail room work and copying. But when it comes to higher-level functions such as accounting and information technology, he has never considered taking the work to outside companies.

"My [chief financial officer] and I have this debate all the time. I'm kind of old school. I want them to be our employees," he said.

Appenzeller's view may be commonly held in Texas, where firms are just tiptoeing into outsourcing, according to interviews with managing partners. They remain tentative about fully moving back-office functions outside the firm, even as some large U.S. firms boast big cost-savings from making such moves.