A golden rule of diplomacy is you don't choose who you deal with. For almost all European leaders, Boris Johnson would be just about the last person they would want to face across the table. But that's who they've got.
A man previously known as a buffoon and a chancer has just secured a mandate that most of his interlocutors would die for. He is going nowhere for at least five years. He will use his majority to embed a populist government in his name and a Brexit that will bear little resemblance to the relationship they enjoyed with Britain.
It is a distasteful and unhappy state of affairs. But they will have to get used to it.
Signs are that they already are. The first clue (or rather lumbering thud) from the prime minister was his decision to enshrine into law the UK's final departure from the EU on December 31, 2020.
It won't be a full exit. It will encompass just the bare bones of the areas previously covered by the EU, but for domestic political reasons that's all he wants.
"We are well advised to take seriously that the UK does not intend to go for an extension of the transition, and we need to be prepared for that," acknowledged Sabine Weyand, the director general of the EU's trade department. "That means in the negotiations we have to look at those issues where failing to reach an agreement by 2020 would lead to another cliff-edge situation."
It is not just the limited scope of future cooperation that is concerning. It is the tone and manner. As Leo Varadkar, the Irish Taoiseach, pointed out, Johnson looked set on a "harder Brexit than we anticipated". The UK, he said, appeared to want to undercut the EU on food, health and product safety.
The Brits don't bother to hide it. Presenting his EU Withdrawal Bill to the new and pliant House of Commons before Christmas, Johnson said it "paves the way for a new agreement on our future relationship with our European neighbours, based on an ambitious free trade agreement. This will be with no alignment on EU rules, but instead with control of our own laws, and close and friendly relations".
Downing Street's calculation is that the more it alarms Europe, the more concessions it will extract. At the same time, they want to relegate the negotiations to a lower level of priority for parliament. After all, trade talks around the world are supposed to be dull.
The EU is quite happy for the negotiations to be unexciting. It has been less than impressed by the British grandstanding over the past three-and-a-half years, the finger wagging, the rudeness, the lack of preparedness seen as symptomatic of a political culture that prizes rhetoric over hard graft and good sense.
They know that the closer the negotiations get to next autumn's deadline the more Johnson will play to Britain's Dad's Army stereotype. The fastest trade deal the EU has secured was with South Korea. That was concluded in 2009 after more than two years of often difficult talks. It took another two years to come into force.
They also know that he will have to choose between two options. It is binary. Any duty-free, quota-free deal would need to contain guarantees of a level playing field in areas such as state aid and competition, environmental and labour law and taxation.
This would go beyond requirements set in recent deals with Japan or Latin America because they are further away and less economically integrated with the EU than Britain.
If he sticks to his vision of Singapore-on-the-Thames, to his no-alignment mantra, he can. But he will then have
to face trading with the EU on WTO terms.
As it has already shown, in its dealings with Johnson and with Theresa May before him, the EU is unfazed by the threat of a breakdown in negotiations. Both sides will suffer, but it knows the UK will be hurt more.
A skeleton deal is likely to focus only on tariffs and quotas in goods. There will be little scope for agreement on services - which are far more important to the UK economy - or on regulation of data flows.
Britain sends roughly 45% of its exports to the EU. Its continued role as a global hub for multinationals - on which so much wealth has been created since the 1990s - will be undermined if it finds itself subject to border controls and tariffs in its dealing with the European continent.
Global companies have for some time been staking out Amsterdam, Paris, Frankfurt, Berlin, Dublin and other cities as an alternative. Several have already moved parts of their operation, or relocated their European headquarters, there.
The area that Johnson and his aides are most confident about in their new pick-and-mix approach to cooperation is security.
It is no coincidence that he made his first trip abroad as super-charged majoritarian prime minister to Estonia, to visit British forces. They are serving as part of Nato's Enhanced Forward Presence, alongside those of France, Denmark and Estonia itself, on the Baltic state's frontline with Russia.
This is just the sort of collaboration he wants to highlight as part of the UK's "global" ambitions. He did, of course, meet Estonia's prime minister on his whistle stop visit.
It would have been rude not to. But the main aim was the photo opportunity for the folk back home, serving food to the squaddies.
Angela Merkel, Emmanuel Macron and the other leaders will have to find a way of working with Johnson, whether through gritted teeth or more warmly than that.
They have been schooled in the art of humouring quixotic populists in their years of dealing with Donald Trump. They've learned that trying too hard doesn't work (the French president's love-in with his US counterpart on Bastille Day didn't get him anywhere), nor does the German Chancellor's icy stare.
They will be pragmatic, taking what they can, giving where they have to. The UK is already far more aligned with its EU neighbours on the key foreign policy issues of the day - climate change, Syria, Russia and China - than it is with Trump. All this marks a return to 19th century arrangements, away from the Bretton Woods dream of international organisations. It worked for 75 years, which isn't a bad run.
The future European choreography contains two paradoxes. The first is that the one partner the Germans have most in common with in Europe is the UK.
Merkel sees much more eye to eye with the Brits (alongside the Dutch and the Nordics) on economic policy than she does with the French. The second is that Merkel and Macron do not get on.
He is frustrated by her caution. She is not enamoured of his flamboyant gestures. However, they know that this relationship is pivotal to both countries.
During a dinner for British diplomats and thought leaders in Berlin earlier this year, Germany's justice minister at the time, Katarina Barley (whose father's side comes from Lincolnshire), gave this candid warning: "Even if we agree with you in the future, we will always be more distant, because family comes first and you are no longer family."
The pain is real, but they have already moved on.
