A US judge has refused to let three bankers return to the UK while awaiting trial, calling them "a flight risk".
The three had agreed to wear electronic tagging devices in London
The ex-NatWest bankers, extradited to the US on fraud charges arising from Enron's collapse, must put up cash or guarantees by 31 July or face jail.
The trio must post $1m (£541,000) or guarantees to secure full bail and must live in the Houston area of Texas.
The trial of the so-called NatWest Three is slated to begin in September although it could be delayed.
US prosecutors have indicted David Bermingham, Giles Darby and Gary Mulgrew on fraud charges but the three maintain their innocence.
At a hearing in a Houston court, US magistrate Stephen Smith said they would not be allowed to return to England pending a trial.
"The problems posed by allowing the defendants to return to the UK are very substantial," he said.
He expressed concern about lack of US jurisdiction if they left, so they "will be restricted to the US".
The three will not be allowed to live together and must remain within the court's jurisdiction, effectively confining them to an area stretching from Houston to the Mexican border.
Mr Bermingham and Mr Darby have to deposit $250,000 (£135,000) each in cash or credit guarantees with the authorities by the end of the month and a further $250,000 by October.
The three men must live within the Houston area
Mr Mulgrew must stump up a total of $200,000 (£108,300) over the same period.
It is not known whether the three men have sufficient assets to meet these requirements or whether they will be able to work in the US during the period.
Mr Bermingham said the bail conditions were tough.
"We are tough people but I am not underestimating the difficulties we face," he said. "It might be regarded as a form of psychological torture if you wish.
"We went into the courtroom this morning hoping and praying we would be able to go back and see our families and that was the first thing denied us."
The three had been free on temporary bail since their initial 14 July hearing, wearing electronic monitoring devices allowing federal officials to track their movements.
Prosecutors say that, in 2000, the three men advised their former employer, NatWest, to sell part of a company owned by collapsed US energy giant Enron for less than it was worth.
They then left the bank and bought a stake in the company before selling it on at a significantly higher price and making a huge profit, it is claimed.
They were extradited under a new fast-track system agreed by the British government and face up to 35 years in prison.
During the hearing, US prosecutors pointed out that the three did not surrender willingly to American authorities and claimed they might not return to court if they returned to the UK.
The men's lawyers said in court papers filed on Thursday that, if granted bail allowing them to live in London, they would waive extradition and continue to wear electronic monitoring devices.
They also said they would remain under the supervision of UK authorities and post a combined $4m (£2.15m) in bail payments signed by friends and family members.