Officials said the new wording represented an attempt to avoid legal pitfalls and ensure Americans were safe from terrorism at home.
Quite a lot. The first ban was criticised for its botched implementation, sparking protests at airports as arrivals with valid visas were detained.
This time, officials spent 24 hours briefing journalists, members of Congress and officials about its new content. It will not take effect until March 16 to ensure other countries, airlines and border guards understand how it works.
The executive order also contains a string of exemptions.
Who will it affect?
Nationals from six countries – Iran, Syria, Libya, Sudan, Somalia and Yemen – are still subject to the ban.
However, nationals from Iraq have been removed from the list after American politicians pointed out that the original order penalised individuals who had worked for US armed forces and raised awkward questions about how Washington treated allies in the fight against Isil.
The order leaves in place a suspension of the US refugee programme for 120 days but drops special treatment of Syrian refugees, who are no longer subject to an indefinite ban.
The new version also now exempts individuals from all six countries who already hold a visa or who have a Green Card and the legal right to live in the US.
What does that mean?
When the original executive order was suspended it came as the result of a challenge by Washington State, which argued that its own interests were harmed by the travel ban.
Bob Ferguson, its attorney general, listed the harms - from separating Washington families and damaging the local economy to undermining "Washington's sovereign interest in remaining a welcoming place for immigrants and refugees”.
His argument brought an emergency stay on the executive order as judges sided with his point that the state, as a victim of the order, had a right to be heard.
By ensuring that residents, workers with visas and students can enter the US, that case will now be much harder to make.
So will there be fresh legal challenges?
Immigration and civil rights groups which brought cases say they are studying the new wording and stand ready to launch fresh legal challenges. Several said the softer tone did not disguise the fact that it was a Muslim ban in all but name.
Salil Shetty, Amnesty International’s secretary general, said: "Removing the ambiguity about permanent residents is simply an attempt to evade further judicial scrutiny. The anti-Muslim rationale behind this executive order should be evident to anyone familiar with Trump’s long campaign to spread fear about Muslims.”
How does the White House defend it?
This time around the order was signed by Mr Trump in private. He lined up three of his cabinet secretaries before cameras to present the case as if to distance the order from his campaign comments on banning Muslims from entering the US.
Jeff Sessions, his embattled Attorney General, said the FBI was currently investigating 300 people who arrived as refugees for terrorism-related activities.
"Three of these nations are state sponsors of terrorism. The other three have served as safe havens for terrorists – countries where the government has lost control of territory to terrorist groups like Isil or al-Qaeda and its affiliates,” he said. "This increases the risk that people admitted here from these countries may belong to terrorist groups, or may have been radicalised by them.
Any problems so far?
Once again the administration has demonstrated its lack of attention to detail. After explaining why Iraq should be exempted from the new regulations, the executive order goes on to give examples of the dangers faced by America from immigrants.
"For example, in January 2013, two Iraqi nationals admitted to the United States as refugees in 2009 were sentenced to 40 years and to life in prison, respectively, for multiple terrorism-related offences,” it says.