Almost no U.S. oil and gas operators working in federal offshore waters have agreed to report “near misses”—the incidents that do not cause accidents but come close. The director of the Bureau of Safety and Environmental Enforcement says he intends to change that.

So far, only three companies out of the 88 operating on the Outer Continental Shelf (OCS) have signed up for the voluntary program, and to date not a single incident has been reported, according to BSEE Director...