The explorer David Hempleman-Adams says he believes he has broken the world altitude record for a balloon with an open wicker basket.
The balloon set off from Colorado in its record-breaking attempt
He reached the target height of 37,000ft (11,300m) one hour and 15 minutes after take-off from Colorado.
The previous record of 35,626ft was set by Per Axel Lindstrand in 1996.
Speaking from Denver, the explorer said he thought he had scooped a total of eight world records and reached an unconfirmed height of 42 or 43,000ft.
Flight director Tim Cole said: "It definitely looks like he has done it but we won't have official confirmation until tonight."
In a crackly radio transmission from the balloon, Mr Hempleman-Adams told the team he believed he had broken the world altitude record for a Roziere balloon.
On the ground in Denver in his first interview after landing, the 47-year-old told the BBC of his success.
"We were trying for 36,000ft but we got the absolute record as well - we got up to something like 42 or 43,300 but we've got to confirm that.
"I was just above the cloud and it was spectacular but it was about minus 80 so I was just concentrating on keeping everything going and breathing.
The ascent is the latest in the explorer's string of challenges
"I was on 'demand oxygen' and it was just too much to look at the scenery.
"Because it was so cold we had a few problems and one or two bits of the oxygen kit froze but that's happened before.
"Because of that we took a triple system - and I'm glad we did.
"The landing was one of my better ones - I didn't take out too many cows here so it worked out OK.
"But it was quite scary and just nice to get landed."
The Mears Altitude Challenge balloon - named after the sponsors of the bid - is 140ft high from basket to envelope top.
It is the same balloon Mr Hempleman-Adams used to complete the first single-handed passage across the Atlantic in September 2003.
The father of three from Box said he had chosen to use the open wicker basket over an enclosed capsule as it was the "traditional" way of ballooning.
He wore an oxygen mask to cope with the high altitude, while the burners of the Roziere-type balloon were specially adapted to deal with the sub-zero temperatures.