After their meeting at the White House, President Barack Obama walked his guest, the Prime Minister of Israel, Benjamin Netanyahu, to his limousine.

The solicitous host waited, slightly awkwardly, as Mr Netanyahu settled himself into the back seat.

Immaculately uniformed servicemen stood rigidly to attention on either side of the vehicle.

And then the video ended, before you could see whether Mr Obama waved until his new pal was out of sight.

Actually he was only staying a few minutes walk away, at the official guest quarters, Blair House.

But it was time to bring the curtain down on the final scene in the day's political theatre.

One last detail was left. The White House released a photo of the two first ladies, chatting in a drawing room decked with flowers.

President Obama does not normally walk his guests to their cars.

The BBC's White House producer, an expert in these matters, tells me he didn't do it when President Nicolas Sarkozy of France was in town, nor when President Dmitry Medvedev of Russia came calling.

And he didn't do it either when Mr Netanyahu was last at the White House in March, which was why the political theatrics were necessary.

Then, President Obama exacted revenge for what one of his top aides had called an insult to the United States.

It was a plan to expand a Jewish settlement in Jerusalem, which had been unveiled a couple of weeks earlier.

Not only did it rub salt into the fact that Mr Netanyahu had refused a request from the White House to freeze all construction for Jews in the occupied Palestinian territories, the plan had been announced while the US Vice-President Joe Biden was visiting Jerusalem.

So that March meeting was held at dinner time, far too late for the evening news in Israel.

Not even a still photo was released. President Obama apparently absented himself for a while to eat with his family.

The Israelis were so stunned, according to the travelling press who flew back with the delegation, that they did not use the White House phone in case it was bugged.

More than three months on, both sides have decided that it is in their interests to make up, very publicly, which was the reason for why the prime minister was treated with such care and consideration.

President Obama said their talks were "excellent" and the relationship between the two countries was "extraordinary" and "unbreakable".

Prime Minister Netanyahu said that reports of the demise of the special relationship between the US and Israel were not just premature, they were "flat wrong".

In the age of political spin, it is always useful to counter criticism by exaggerating it.

I don't recall any serious commentators saying that relations between Israel and the US were breaking down. Plainly, the links between the two countries are far too strong for that.

It was not simply that Mr Netanyahu appeared to be getting under the skin of Barack Obama in the same way that had alienated Bill Clinton in the 1990s.

The fact is that despite the tableau that was played out at the White House on Tuesday this week, there is plenty of evidence that the relationship between the two countries is changing, even though their political, historical and cultural DNA remains inextricably linked.

The Israeli ambassador in Washington was reported to have briefed his foreign ministry that there was a tectonic rift between the two countries.

Meir Dagan, the boss of Mossad, Israel's secret intelligence service, told a committee in the Israeli parliament that his country was gradually turning from an asset to the United States to a liability.

A leading strategist in Washington wrote recently: "It is time Israel realised that it has obligations to the United States, as well as the United States to Israel."

The reason for all this was stated plainly at the start of the year by the US General, David Petraeus.

He said that anti-American sentiment in the Middle East was exacerbated by perceptions of US favouritism towards Israel.

Anyone who has spent time in the Middle East would take that as obvious tending towards the banal.

But to hear it from the mouth of America's favourite general was something else.

When President Obama took office, a calculation seems to have been made that his predecessor President Bush had been over-indulgent to Israel.

Combined with the deadly bungling that followed the invasion of Iraq, it meant that the US policy in the Middle East was harming America's own interests. Something would have to change.

The president appears to be an intellectually consistent man - the word professorial is used about him as a term of abuse by some of his critics in the United States - so unless he has performed a gigantic flip-flop, there is no reason to suppose that his views have been altered by a more civil couple of hours with Mr Netanyahu.

In their statements, they skirted round potential disagreements.

Neither man would give a straight answer to one of this moment's key questions: would Israel continue the partial freeze on the construction of homes for Jews in the occupied Palestinian territories which is due to finish in September?

Half a world away in Finland, Israel's nationalistic foreign minister Avigdor Lieberman said it would end.

That is not necessarily definitive, but it reflects a strong view in Mr Netanyahu's coalition.

President Obama avoided the question of extending the partial settlement freeze by saying that well before September Israel and the Palestinians would be talking face to face.

At the moment all the Americans have to show for 18 months of trying are indirect talks between Israel and the Palestinians, in which the US envoy George Mitchell shuttles between Jerusalem and Ramallah.

Big tests lie ahead. In the public part of the meeting at the White House they didn't say much that was new about Iran and their reaction to its nuclear ambitions.

But the most significant unanswered question in the Middle East is still whether Israel will bomb Iran's nuclear facilities.

The Obama Administration has declared that peace in the Middle East is a strategic interest of the United States. It is not close at all at the moment.

But if President Obama is still serious about trying, then he must know that he will need to do some arm-twisting - of his Israeli friends, as well as his enemies.