Small U.S. oil companies are shutting off wells faster than expected, as prices fall below what it costs them to pump the crude out of the ground.

The collapse that sent U.S. benchmark prices into negative territory last week persuaded many smaller-scale, privately held drillers to shut many of their wells until the economy revs up again and demand bounces back. These drillers—in places like West Texas, New Mexico, North Dakota, Wyoming and Louisiana—collectively account for about a quarter of American production.

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