Two other small tremors were felt in May, and three others hit the area in early June, according to the U.S. Geological Survey.
Cleburne officials are working with researchers from Southern Methodist University to determine if nearby gas drilling is causing the quakes.
No damage or injuries have been reported in any of the tremors.
Cleburne, a town of about 22,000 people, is about 50 miles southwest of Dallas.
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