PALM BEACH, Fla.—A record dry season left West Palm Beach, Fla., with just 22 days worth of fresh water last month, prompting new rules restricting residents to once-a-week watering schedules for lawns and plants.

But with a 2.6-acre estate in neighboring Palm Beach that features a 37,000-square-foot home, a pool and lush tropical landscaping, Terry Allen Kramer is accustomed to using more than 120 times the amount of water consumed by the average customer in the region.