With thousands of oil wells choking back or completely shutting off production, companies already are looking ahead to what may prove to be an even bigger challenge: turning wells back on. U.S. and Canadian oil producers are curbing as much as 4.5 million barrels of daily supplies, according to Plains All American Pipeline LP. In the U.S. alone, drillers have announced plans to halt more than 600,000 barrels of daily output this month and next, said Rystad Energy AS. Old-style, conventional wells were the first to go down and the closures are expanding to some of the horizontal gushers that represent shale drillers’ prize assets.

Although shutting down a well can be a relatively simple — and even remote-controlled — process, industry executives and their engineering teams aren’t altogether sure how smoothly an idle well can be restarted. “When you shut in wells, especially for a long period of time, you have a lot of surprises,” Clay Bretches, an executive vice president at Apache Corp., said during a conference call with analysts on Thursday. “Some of them are good and some of them are bad.”

Executives are careful about disclosing which wells are being curtailed — which involves squeezing back on the volume of crude flowing out of the well — versus those that are completely shut down. That’s because reversing a total shutdown presents a more challenging set of tasks and costs.