Standing next to a frequently baffled-looking German Chancellor Angela Merkel, President Trump told how he saved the United States more than $999 million on the embassy he plans to build in Jerusalem.

This is the story he told:

They came to me with a proposal for a $1 billion embassy in Jerusalem. And the papers, Mike Pence can tell you, the papers were put before me to sign an application for more than $1 billion to build an embassy. I said, “What are you talking about, a billion dollars?” You know, most embassies are, like, a single story. And they said, “Yes, sir, it’s $1 billion.”

I had my name half-signed, then I noticed the figure, and I never got to the word “Trump.” I had “Donald” signed, but I never got to the word “Trump.” And I called my ambassador, who’s a great lawyer. Most people in business know David Friedman; he’s the ambassador to Israel. Loves Israel. Loves our country; loves Israel, too.

I said, “What’s this one billion?” He said, “I can build it for $150,000.” I said, “What?” He said, “I can build it for $150,000, the embassy. We have a building, we have the site, we already own the site, we own the building. I can take a corner of the building, and for $150,000 we can fix it up, make it beautiful, open our embassy — instead of in 10 years from now, we can open it up in three months.” And that’s what we did.

But I said, “David, let’s not go from a billion dollars to 150 thousand, let’s go to three, 400,000.” We take a piece of the building. It’s going to be beautiful. And it will be somewhat temporary, but it could be for many years, because by the time they build it the other way it’s gonna be many, many years.

They were looking for sites? We already have a site.

To a casual observer, that story can be summarized as follows: A plan to spend $1 billion on an embassy got to Trump’s desk, and he noticed the price and balked. Instead, the ambassador to Israel suggested using an existing site for which the cost would be only $150,000. Trump suggested a bit more than that be spent but that the plan move forward. The result? A beautiful facility upholding Trump’s pledge to move the embassy from Tel Aviv to Jerusalem for 0.04 percent of the planned price.

But this, it seems, isn’t really what happened.

First of all, Trump has told this story before. In early March, during a meeting with Israeli Prime Minister Benjamin Netanyahu, Trump made the same claim about being presented with a $1 billion bill that he rejected. At that point, Trump said the actual cost would be $250,000, not $400,000.

Second, Trump’s depiction of what’s happening appears to glamorize the reality. To speed the process of transitioning from Tel Aviv to Jerusalem, the United States will be upgrading an existing facility in Jerusalem. The New York Times reported in February that the first phase — the phase that would be complete in the three-month window mentioned by Trump on Friday — would be to “carve out some office space for Ambassador David M. Friedman and a small staff.” Then, by the end of 2019, the existing compound will be expanded to increase the available office space. In order to meet a May timeline, the Israeli government fast-tracked permitting to build a new wall and escape route at the compound.

In the meantime, the Times reported, the government will still be looking for a site for a permanent home to the embassy. (Trump notes that the existing solution is temporary but quickly glosses over it.)

When Trump told the story in March, the White House press corps asked press secretary Sarah Huckabee Sanders what he was describing when he mentioned spending only $250,000.

“I’ll have to get more specifics,” Sanders replied. No additional specifics appear to have been forthcoming. Sanders continued: “I think the point he’s making is that he’s going to do it faster and far less expensive than a billion-dollar project, as was projected.”

Well, sort of. Let’s say you need somewhere to live and plan to build a house. You estimate that building that house will cost you $250,000. In the meantime, you rent a studio apartment for $400 a month. If you’re still planning on building that house, you didn’t save $249,600, you just postponed spending it — and no matter how nice you make your rental apartment, it’s probably not going to have the bells and whistles of your completed house.

Perhaps this plan to build out the existing compound in Jerusalem will end up being the permanent, long-term solution, and the total cost — presumably higher than $400,000 once the additional office space is built — will come far short of $1 billion. But here Trump seems to be trying to have his cake and eat it, too. Either you’re going to spend millions or hundreds of millions of dollars on a new, ground-up facility, or you’re not. You don’t get to claim credit for saving money by going with a short-term solution if you’re still planning on spending a ton of money on a long-term one.

As for the thing about Trump getting halfway into signing his name before he stopped? A reminder to always read documents before you sign them.

This article has been corrected to clarify where the upgrade is taking place.