One of the more memorable quotes of the Brexit saga was ascribed to an anonymous source within the Democratic Unionist Party (DUP), in Northern Ireland.
"This is a battle of who blinks first - and we've cut off our eyelids."
Since the historic defeat of her Brexit deal, which was rejected by 230 votes in the Commons, Theresa May has come under pressure to alter it.
She said she would ask Brussels for "legally binding changes" to the most controversial part of the Withdrawal Agreement - the backstop - the insurance policy which aims to stop the return of a hard border between Northern Ireland and the Irish Republic, after Brexit.
At the moment the EU is saying that the deal on the table, painstakingly negotiated for more than 18 months, is as good as it gets.
So what form does the EU have on renegotiation? Has it blinked in the past? There are no exact comparisons, because Brexit is a unique situation. But here are a few examples:
Denmark narrowly rejected the EU's Maastricht treaty in 1992 and subsequently negotiated four optouts from Maastricht on:
- joining the euro
- EU citizenship
- justice and home affairs
- a common defence policy
The optouts were contained in a legally binding protocol to the treaty but the main body of the text was not changed.
In a second referendum, in 1993, Denmark voted in favour.
Ireland has lived through two referendums on the same issue on two separate occasions.
In 2001, the country voted against the EU's Nice Treaty, mainly because voters were concerned that Irish military forces would have to take part in Nato-led peacekeeping operations.
The text of the treaty was not changed but the Irish government issued a national declaration reaffirming its military neutrality.
In a second referendum in 2002, the Nice Treaty was approved by an overwhelming margin.
Again, in 2008, Irish voters rejected the Lisbon Treaty, citing concerns about tax, abortion and military neutrality.
A second referendum, in 2009, approved Lisbon after promises were made to address these concerns.
They eventually formed a protocol that was approved in 2012 but the text of the Lisbon Treaty itself was not changed.
In 2016 an advisory referendum in the Netherlands rejected an EU trade and cooperation agreement with Ukraine. The Dutch government needed legally binding assurances from the rest of the EU before it could get the deal approved in parliament, and it got them.
They came in the form of a declaration spelling out the fact that the agreement did not make any guarantee to Ukraine of future EU membership, nor did it oblige the Netherlands to provide Ukraine with military assistance.
But the agreement with Ukraine was not changed in any way, and an equivalent outcome for the Brexit deal would fail to satisfy many Eurosceptic MPs in Westminster.
A draft EU constitution was signed by all member states in October 2004 and ratified by 18 countries before being rejected in referendums in France and the Netherlands in 2005.
After licking a few wounds, the EU came up with the Lisbon Treaty, which kept many of the main provisions of the draft constitution, including a new president of the European Council and a clause on withdrawal from the EU (Article 50).
But it dropped the name "constitution" itself and it didn't include references to EU symbols, such as the flag and the anthem, that would normally be associated with a state.
The rejection of the constitution led to what were probably the biggest changes the EU has ever made in treaty negotiations but critics say Lisbon was still as close to the proposed constitution as it could get.
Greece was pushed into a financial bailout programme in 2010, accepting huge loans from the EU and the International Monetary Fund (IMF) in return for drastic austerity measures, including tax rises and sweeping cuts in spending and pay.
After a new government led by the radical left-wing party Syriza took office in 2015, it held a referendum in which it campaigned for an end to EU-imposed austerity.
Despite substantial backing from Greek voters, Brussels (and Berlin) didn't blink.
Austerity continued and the government had to apply for another bailout loan in order to stay in the eurozone.
In the run-up to the Brexit referendum in the UK, the then Prime Minister, David Cameron, tried to renegotiate aspects of the UK's membership of the European Union, in order to show voters that reform was possible.
He won recognition that the UK could opt out of the EU's founding ambition to forge an "ever closer union" and he was given guarantees about the rights of EU countries outside the eurozone and vague promises to cut red tape.
But even though he also negotiated some limits on the ability of EU migrants to claim benefits, he failed in his push for more far-reaching changes to EU freedom of movement rules.
Mr Cameron's renegotiation was largely ignored during the referendum campaign, even though EU officials argued that they had pushed EU law to the limit in an effort to accommodate him.
As has often been the case in negotiations between the EU and the UK, the maximum the EU was prepared to offer was less than the minimum than many supporters of Brexit were prepared to accept.
Is history about to repeat itself?
This piece was updated on 29 January to reflect Theresa May's statement to the House of Commons.