MOJAVE DESERT, California (CNN) -- SpaceShipOne achieved its most spectacular flight yet, climbing to an altitude of 364,000 feet (70 miles), eight miles beyond what was needed to win the $10 million Ansari X Prize.

With a wish of "Good luck and Godspeed," mission control sent the privately funded craft toward space for the second time in a week, the requirements for winning the X Prize.

"Today we have made history. Today we go to the stars," said Peter Diamandis, co-founder of the X Prize Foundation.

The $10 million award is intended to spur civilian spaceflight.

The craft left a near perfect dove-tail of exhaust contrails with the White Knight turbo jet, which carried it aloft, as its rocket ignited for 84 seconds. The rocket burn sent SpaceShipOne on a trajectory that sent it climbing for almost a minute after the engine shut down.

"It looks great," said Brian Binnie, SpaceShipOne's pilot, on his way up to space at Mach 3.

Binnie reported a shaky flight with "a little roll" but did not experience the 29 rolls Mike Melvill experienced last week.

Space ShipOne and White Knight, featured a new paint job promoting Virgin Group, Richard Branson's firm, which recently announced a deal to license the SpaceShipOne technology for a fleet of commercial spacecraft

Spacecraft designer Burt Rutan told a crowd gathered at his home in the Mojave Desert on Sunday that he was confident of the success of today's flight -- and winning the $10 million Ansari X Prize check.

After some unexpected acrobatics during the last flight, Rutan said Monday's would be a smooth flight, but he was prepared for stability issues.

"We believe we have solved these and we don't believe we'll see the rolls tomorrow," he said. "But if we do, we don't believe they're dangerous. ... After all, what we're doing is research."

Binnie, who piloted the first powered SpaceShipOne launch, was at the helm of the craft after it was released from the belly of the White Knight turbojet at about 50,000 feet.

Within seconds after igniting its rocket, it was traveling faster than a bullet out of a rifle.

The spacecraft was outfitted with a stronger engine and some aerodynamic modifications from its first record-breaking flight into space on June 21.

Melvill flew the craft's first mission to space and reached, just barely, the required 62-mile altitude, passing the internationally recognized boundary of space. Wind shear and a jammed control on the tail meant the craft veered about 20 miles off course, but it returned for a smooth landing. It was only SpaceShipOne's fourth flight using the rocket engine

On Wednesday, SpaceShipOne streaked even higher to 337, 569 feet (64 miles). However, during its ascent, the private spacecraft began a series of rolls that Melvill brought under control only after ending the rocket burn 11 seconds early.

SpaceShipOne's thrust was provided by two innocuous substances that, when mixed together, are explosive: nitrous oxide and rubber.

A fuel tank about six feet in diameter at the center of the craft holds liquid nitrous oxide, also known as laughing gas. A hollow tube leading from the tank to the engine nozzle is filled with solid rubber. The combustive combination produces thousands of pounds of thrust, although exact amount remains secret.

Most importantly, says aerospace engineer and spacecraft designer Rutan, it has opened the world -- and a private market -- to spaceflight.

"I strongly feel that, if we are successful, our program will mark the beginning of a renaissance for manned space flight," said Rutan in an X Prize statement.

The nonprofit X Prize Foundation is sponsoring the contest to promote the development of a low-cost, efficient craft for space tourism in the same way prize competitions stimulated commercial aviation in the early 20th century.

The prize is fully funded through the end of the year.

Branson, chairman of Virgin Atlantic Airways, announced last Monday that he would invest $25 million in a new space venture, to be called Virgin Galactic. The project will license Scaled Composite's SpaceShipOne technology for commercial suborbital flights starting at about $200,000.

Branson expects it could fly 3,000 people within five years.

"The development will also allow every country in the world to have their own astronauts rather than the privileged few," he said.