Arizona is the odd state out in agreeing to dramatically curtail water use from the Colorado River, raising tensions in the Southwest as extreme drought conditions return.

At issue are falling water levels at the West’s biggest reservoir, Lake Mead. Having already dropped by more than 150 feet over the past two decades to 1,077 feet, the Nevada reservoir is two feet shy of falling below a federal threshold that can trigger mandatory cutbacks by U.S. officials.

Nevada,...