"There's no doubt that the ultimate solution is a relief well," BP CEO Tony Hayward said.

Since 1969, oil companies have drilled seven deepwater relief wells in the Gulf of Mexico - all but one of them successful - although BP's current drilling would be the deepest ever.

"They're not reinventing the wheel, if you will," said retired Coast Guard Adm. Thad Allen. "It's something they've done before."

BP's challenge? Make it work, without making it worse. Around the clock, the two relief wells sink lower, reports CBS News correspondent Mark Strassmann. Both run parallel to the gushing well. One is two weeks ahead of the other, now 17,000 feet below the Gulf's surface. Nine hundred feet lower, electromagnetic sensors will find the best spot for a diagonal cut into the broken well bore, the most precise step of all. Then four pumps will push in heavy mud, to overcome the broken well's ferocious upward pressure. And finally, cement, to plug it permanently.

"It's not a solid dunk," said Eric Smith, a deepwater drilling expert. "It's going to take some work."

Smith said two things could go wrong. The cut could miss the broken wellbore, and BP would just try again, or engineers could drill into hidden gas pockets.

"When you are drilling into that you have to be careful of a kick, a blowout in the relief well," Smith said.

BP leaders have showed supreme confidence in their relief wells.

"I fully expect that the well itself will be shut off in August," said Bob Dudley, BP's point man on the spill.

But recently? More caution.

"The drilling of relief wells, there's nothing guaranteed," Dudley said.

And if this fix fails?

One reported option is sub-sea pipes, to pump contained oil to a platform several miles away.

"I'm actually pretty confident they'll get it on the first pass," Smith said.