Privateer Elon Musk has launched his budget rocket, Falcon-1, from the Kwajalein Atoll in the South Pacific.
This was the second attempt to send the rocket into space
The 21m-long vehicle lifted off at 1810 California time (0110 GMT) and rose to an altitude of 320km (200 miles).
Mr Musk, who co-founded the internet financial system PayPal, wants to lower the cost of access to space.
The flight did not achieve all its goals, but he said it demonstrated the vision of his Space Exploration Technologies Corporation (SpaceX).
The mission was the second attempt to loft the rocket; the first, in March 2006, ended when a fire fed by a fuel leak led to the shut down of the main-stage engine just 29 seconds after lift-off.
On the latest flight, the second stage did not achieve its full speed, again because of an early shut down of the engine, this time because the vehicle began an unexpected roll.
Mr Musk said he thought this problem should be easy to fix once flight engineers had analysed the data.
"The launch was not perfect, but certainly pretty good," he added.
"Given that the primary objectives were demonstrating responsive launch and gathering test data in advance of our first operational satellite launch later this year, the outcome was great."
The Falcon-1 is the first in a line of vehicles the SpaceX company hopes will shake up rocket services.
It is a two-stage rocket powered by liquid oxygen and kerosene. The first stage is designed to parachute into the ocean to be recovered and used again.
With the relatively low price of about $7m (£4m) per flight, the Falcon-1 is making a serious attempt to undercut other players in what is an overcrowded launcher market.
The largest rocket planned by SpaceX is the 53m-long Falcon-9, which should be able to carry about 25,000kg (55,100lbs) into low-Earth orbits.
This would put it in a similar class to current American vehicles such as the Delta 4 or Atlas 5, and the European Ariane 5.
SpaceX was recently given a $278m (£142m) award from the US space agency (Nasa) to demonstrate cargo delivery services to the International Space Station.
The company says it also has satellite launch commitments on its books worth about $400m (£200m).
Although started by Mr Musk, the PayPal electronic payment system is now owned by the internet auction site eBay.