WASHINGTON - Navy SEALs' attempted Dec. 6 rescue of American hostage Luke Somers in Yemen quickly went awry when a barking dog apparently alerted guards and a 10-minute firefight erupted. U.S. officials said an al-Qaeda in the Arabian Peninsula militant raced ahead of the raiders and shot Somers and another hostage, South African schoolteacher Pierre Korkie. Both died.

The disappointing outcome, one of three unsuccessful rescue missions this year, highlights a new willingness by the Obama administration to try to save Americans held by terrorist groups despite risks that once would have been considered too great, senior U.S. officials said.

That willingness was given greater impetus this fall by grisly videos of the beheadings of Americans and others held captive by Islamic State militants in Syria, officials said.

It also rests on the growing realization in the White House that, unlike in times past, rescuers can't wait until they are certain where hostages are and until the Pentagon, FBI, and intelligence agencies have high confidence about their ability to rescue them.

"We've needed to go out with imperfect intelligence and imperfect conditions to have any chance of saving American lives," said a senior military official who spoke on condition of anonymity in discussing classified operations. "And that means there's that much more risk of failing."

Prompted in part by complaints from hostage families, the White House last month said it had begun a review of how the government handles such cases. But officials said the review is unlikely to lead to a recommendation to lift the U.S. prohibition on paying ransoms, as many other countries do to get their citizens home.

Nor, Pentagon officials said, is the review likely to lead to the constraint of rescue efforts. Islamic State militants are believed to hold at least one other American hostage, an aid worker abducted in Syria last year.

The new U.S. risk-taking began last summer when U.S. special operations troops swarmed into a compound in Syria where journalists James Foley and Steven Sotloff were believed to be imprisoned.

Army Delta Force commandos took a week to rehearse the operation and move from Fort Bragg, N.C., to the Middle East for an assault on the compound. They landed in helicopters on the night of July 3 and engaged in a firefight with militants.

But Foley and Sotloff weren't there. The subsequent beheadings of Foley and Sotloff, shown in gruesome videos posted by their captors in August and September, quickly changed the calculus for President Obama and his advisers as they considered the dangers of rescue operations.