Producers are already restarting oil wells in North Dakota as prices come off record lows, but talk of a recovery is premature, said the state’s energy regulator.

The historic price rout has in recent weeks curbed output in the second-biggest producing state by a third to below 1 million barrels a day, according to the Department of Mineral Resources. More than 7,000 wells have been shut. Now, with prices hovering close to $30 a barrel, field inspectors are reporting that some production is returning.

“The price is signaling to operators, hey maybe we should return some wells to production,” said Lynn Helms, director of the Department of Mineral Resources. But the storage overhang means “we could see a lot of volatility over the next few weeks.”

The drilling collapse in North Dakota can be seen in the rig count which has slumped to 12 from as high as 54 in February. And four or five more rigs could be shut before the slowdown plays out, said Helms. That’s the least since before the Bakken play started up in 2006. The number of frack crews has dwindled to just one from 25 before the crash.

Production in March, the latest month for which the state has complete data, slipped 1.6% to 1.429 million barrels a day.

It will take months to whittle down a national supply glut, so operators shouldn’t be thinking of returning a “significant volume” of production until the fourth quarter, said Helms. That will be winter in North Dakota and adverse weather conditions could delay any ramp-up of activity.

Regulators are set to hold a hearing in North Dakota on May 20 to determine the oil price at which surplus supply “constitutes waste” and consider what relief may be needed.