Theresa May with the President of the European Commission Jean-Claude Juncker | Thierry Monasse via Getty Images | Thierry Monasse via Getty Images May and Juncker dive into Brexit fine print The two leaders focus on changes to the Political Declaration in a joint statement after their Brussels meeting.

Brexit, and the leaders trying to make it happen in an orderly fashion, have now entered the realm of fine print and minutiae.

But they still don’t have a deal.

After a meeting Wednesday evening, U.K. Prime Minister Theresa May and Commission President Jean-Claude Juncker issued a joint statement pledging to continue exploring “alternative arrangements” to the controversial Northern Ireland backstop and “legal assurance” about its temporary nature.

Notably, the statement focused on changes to the Political Declaration, the non-legally binding document that accompanies the 585-page Withdrawal Agreement.

It is still unclear how far May and Juncker's negotiators will get. Officials said the process is inching forward — and in focusing on the Political Declaration it appears that May has taken a crucial step in acknowledging that the Withdrawal Agreement agreed in November would not be reopened.

That is significant because May's Brexiteer backbenchers and the Democratic Unionist Party MPs who support her government have been adamant publicly that only changes to the legally binding document itself will suffice to bring them on board.

The so-called Brady amendment, which was narrowly passed by the House of Commons and launched the prime minister's efforts to renegotiate the backstop, specified that it should be replaced by "alternative arrangements."

In their statement, the two leaders said they explored “which guarantees could be given with regard to the backstop that underline once again its temporary nature and give the appropriate legal assurance to both sides” and they “reconfirmed their commitment to avoiding a hard border on the island of Ireland and to respect the integrity of the EU’s internal market and of the United Kingdom.”

They added, “The Prime Minister acknowledged the EU’s position and notably the letter sent by President [Donald] Tusk and President Juncker on 14 January.”

That letter, to May, stated that the Withdraw Agreement is not renegotiable. "We are not in a position to agree to anything that changes or is inconsistent with the Withdrawal Agreement," the two EU leaders wrote at the time.

The May-Juncker statement Wednesday is notable for its positive tone, though. “The two leaders agreed that talks had been constructive, and they urged their respective teams to continue to explore the options in a positive spirit,” it said.

“They will review progress again in the coming days, seized of the tight timescale and the historic significance of setting the EU and the U.K. on a path to a deep and unique future partnership.”

It added that May and Juncker will speak again before the end of the month.