On May 29, President Barack Obama had lunch at the White House with former Secretary of State Hillary Clinton. The likely 2016 presidential contender has been to hundreds of West Wing meetings, first as first lady, then as senator, and finally as the top American diplomat.

But this face-to-face was unusual. Unlike dozens of presidential meetings every week — and a similar Obama-Clinton meeting in July 2013 — it was not announced in advance.

Instead, reporters who cover Obama learned about the secret visit from a People magazine tweet, and ultimately managed to wring a terse sentence from an anonymous White House official grudgingly confirming that the world’s most powerful person had met with the woman who is arguably the front-runner to succeed him. The topic of their discussion was not revealed.

This is how the White House works. A week before the secret lunch, the schedule failed to mention that the president was hosting a bipartisan delegation of senators for what one Republican attendee later described as a “bizarre” foreign policy meeting. A month before that, there was no advance word that Obama would welcome a group of Japanese-American World War II veterans in the Oval Office — on the eve of the anniversary of FDR signing the infamous order to put Japanese-Americans in concentration camps, no less.

All of those meetings fall well within the president’s duties. But not one appeared on the public presidential schedule posted online the night before and distributed to the press. Instead, all were on the only White House schedule that really matters: the president’s private schedule.

It’s a document so closely held that Obama aides, like their counterparts under George W. Bush, are expected to dispose of it at day’s end in “burn bags” typically reserved for documents so sensitive they cannot be consigned to mere shredding.

Where the public schedule blares “for immediate release,” every page of the private schedule warns: “This schedule contains sensitive information and is provided for your information only. It may not be distributed, forwarded, or printed without the express written permission of the Director of Scheduling.”

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Yahoo News spoke to current and former aides to Obama, George W. Bush, and Bill Clinton to try to find out how the White House puts together the most important document you’ve probably never thought twice about. None wanted to be quoted by name as sharing details from the behind-the-scenes process.

A mock presidential schedule, nearly identical in format to the one President Obama receives. (Yahoo News/Gordon Donovan)

The private schedule embodies a president’s political and public-policy priorities, the full range of challenges or crises he faces at home and abroad. It blends the White House’s needs and wants as the president balances foreign threats against dinner with the kids and meetings with friends. The public schedule is what the White House wants people to know about the president’s day. The private schedule is what he actually does with one of his most scarce resources.

“The most valuable asset in any White House is not money, it’s the president’s time,” explains Josh Bolten, who served as George W. Bush’s chief of staff from 2006 to 2009.

Here’s how that time is blocked out: Every night, around Obama’s 6:30 p.m. target time for dinner with his family, senior aides get a fairly complete schedule for the next day.

“It’s not ‘final,’ because things can change very quickly — we can add or drop events, something might blow up overnight that he has to address,” according to one former Obama administration official.

Every morning, before 7 a.m., “a presidential briefing book” lands with a thud on the desks of “a small handful of senior aides.”

The briefing book is not really a book, more like a thick collated sheaf of 8½-by-11-inch sheets of paper with a colored top sheet emblazoned with the presidential seal and the name of the staff member to whom it is destined.

The Obama schedule shown above accurately reflects the format of the president's daily schedule as seen by senior West Wing aides — but it's for a fictional day, with fictional events, and omits the names, titles, and phone numbers of specific aides. It also has many more gaps than the president's typical schedule. Yahoo News wanted to capture the look, language, and feel of the schedule as accurately as possible, without presenting an exhaustive account of a hypothetical day.

For a sample of schedules from an earlier administration, here's this actual example from the Clinton presidential library.

Throughout the day, top staff today can consult a shared electronic document, made with scheduling software, that reflects any last-minute changes.

That’s a technological leap forward from the George W. Bush era, when the most senior staff got a printed West Wing index card in the morning that had the president’s schedule broken down into five-minute increments, including five-minute buffers between meetings. One former senior Bush aide recalled schedule updates being done in a shared Microsoft Word document.

Aides to Obama and Bush underlined that the schedule isn’t a minute-by-minute straitjacket. “Guy wants a snack. Guy needs to use the bathroom,” one source said with a shrug, explaining why there’s always a little bit of give. An aide to Clinton, asked about keeping a president so notoriously at war with punctuality on schedule, just laughed.

But Clinton’s daily private schedules, made public years after he left office, provide an interesting glimpse into the amount of detail those documents provide — and also what even they fail to record about the comings and goings of one of the most closely watched figures in the world.

Bill Clinton’s private schedule for Dec. 19, 1998, the day he was impeached by the Republican-held House of Representatives, is pretty spare. It lists a 9:40 a.m. briefing in the Oval Office Dining Room, a taping of his weekly radio address at 10:06 a.m., “DOWN TIME” from 11:15 a.m. to 6:30 p.m., and then a black tie holiday dinner from 6:30 p.m. to 11:00 p.m.

What it omits: Clinton’s dramatic Rose Garden address to the nation, in which he refused to resign. Reporters found out at the last minute that the president would be making those remarks — though one source who was a White House aide at the time told Yahoo News that no one in the West Wing was surprised by the House vote.

At other times, the private presidential schedule is notable for the degree of detail it provides for staff — and to historians.

Clinton’s schedules for fundraising events around the August 2000 Democratic National Convention include details like “Goldie Hawn makes brief remarks,” “Sugar Ray performs,” “Cher introduces Muhammad Ali and Mrs Ali,” and “John Travolta makes remarks and introduces the President.”

A few weeks later, a schedule noted that “the President has the option to proceed through buffet line before taking his seat.” Golf entries on the schedule include the names of the first foursome.

The demands on a president’s time are relentless and frequently require tough choices. “There are so many claims on the president’s time. They will come from policy people, the legislative people, the national security people, the public diplomacy people, Congress, agencies … everybody wants a piece of the president’s time,” said one former senior Bush aide, who compared the process of prioritizing the president’s time to wrestling with “a Rubik’s cube.”

Fundraisers are the lifeblood of politics. There are unavoidable international summits, like annual NATO gatherings. Cabinet members want face time, or for the president to champion their goals in public. Aides want face time. Political supporters want face time. Lawmakers want to get the president on the phone. Candidates want the president at their side. World leaders want to visit or host the president on their own turf. There are natural disaster sites to visit. International crises may require the commander in chief to speak out.

So how do individual events get on the schedule?

Many of the competing claims come through the White House scheduler’s office — “an entire office of people who do nothing but” compile demands on the president’s time, according to one former senior White House official.

A look at the White House’s 2014 report to Congress on staffer salaries finds at least 9 aides identified as playing a role in presidential scheduling, starting with Danielle White (formerly Danielle Crutchfield), who was assistant to the president and director of scheduling and advance, and made the same $172,200 annual salary as far better-known aides. She did not return an email requesting an interview.

The scheduling office, helped by policy officials in the executive office of the president, handles most routine requests.

“The last guy responsible for the schedule is the chief of staff, though in some fashion it gets approved by the president,” said a former senior official.

The chief of staff also generally has final say on the duration of events, though for some logistical matters, like the amount of time a given motorcade trip will take, the White House relies on Secret Service estimates.

In the George W. Bush era, there was a whiteboard for blocking out presidential time. Four of them, actually, housed in a cabinet specially built in the deputy chief of staff’s office at Bolten’s request.

“It was very low-tech,” a former official said. “We had a little fold-out cabinet that, when you opened it up, had four big panels. You could get four months of physical whiteboard calendars into this one structure.”

Top Bush aides — chief of staff, deputy chief of staff, communications director, and others — would huddle for at least 90 minutes each week, to ponder, “Are we using the president’s time correctly?”

“So we’re saying the policy people are arguing we need to do a Medicare speech. The communications folks agree. The leg[islative] affairs folks are saying, ‘Oh please don’t do it then,’” the former official recounted.

Bolten pushed for the president to have three to four detailed policy conversations of about 45 minutes each per week, in addition to regular briefings on national security or economic issues. Sometimes those segments were based on the headlines, sometimes designed to defuse potential problems bubbling up between key agencies. “On an issue like fracking, hypothetically, you might have some tension between the energy secretary and the head of EPA, and we could address that this way by having the president’s personal weigh-in,” a senior official recalled.

In the Bush era, every Cabinet officer got personal face time with the president at least twice a year, for half an hour. Those who failed to get to the point quickly, a former aide recalled, would face a warning from the president: “You’re losing altitude and air speed.”

In the Obama era, the White House has emphasized that the president has regular lunches with Vice President Joe Biden and frequent meetings with top Cabinet secretaries.

Having a rigorous, multilayered scheduling process helps ensure that individual Cabinet secretaries aren’t “doing an end run around the policy process,” one source explained. The fact that they can’t reach the president directly assures that they can’t cut out key aides or internal rivals for influence.

“Unless you’re a buddy, and there probably shouldn’t be too many of those, you shouldn’t get on the president’s schedule without other folks knowing about it,” said a former senior official.

In classic Washington fashion, there are also presidential meetings called “drop-bys” that sound casual but are actually meticulously planned. Sometimes a meeting gets that label to dampen expectations that the president will stick around for a long time. Other times, there are questions of protocol — for example, it’s appropriate for the national security adviser to schedule a meeting with a given ambassador or international figure who might not rate a formal sit-down with the president. Then the president just “drops by.”

In campaign season, there are “OTRs” — which get their name from the initials for “off the record,” even though they are only “off the schedule.” Those are stops in restaurants or bars for a bit of schmoozing with people White House aides tend to dub “ordinary Americans.” Technically, Obama’s recent spate of seemingly impromptu walks off the White House grounds — the ones on which he loves to declare that “the bear is loose” — also fit the bill. (Those walks are not announced in advance for security reasons, much like Obama’s unannounced trips to visit American military installations in combat zones.)

Rules and routines may help manage a president’s time, but there is bipartisan agreement across the last three decades that “there is no typical day at the White House.”

“Stuff happens every single day that you need to jump onto in the news,” said one former official. “The space shuttle,” said another. “There are natural disasters, like wildfires, or tragedies like Oklahoma City,” said a Clinton adviser.

“There are always some gaps in the president’s schedule” and ways to adjust it, said a former Bush aide. “He’ll get mad at me, but I’ll shorten his exercise time from 50 minutes to 40.”

“If Iraq all of a sudden goes to s--t, you need to put into the president’s schedule a National Security Council meeting,” observed a former top official.

It’s generally not good news when the president’s schedule makes news. Bush took heat for spending nearly the entire month of August 2001 on vacation at his ranch in Crawford, Texas. Obama’s critics slammed him for attending campaign events in the aftermath of the deadly attacks on American facilities in Benghazi.

And on at least one memorable occasion, the actual physical schedule took an unfortunate spin in the limelight when an insider’s note, intended to be funny, reached the wrong people — the press.

It was October 2001, and President Bush was traveling to China. In the cavernous Shanghai hotel ballroom serving as the media “filing center,” Bush aides suddenly swarmed reporters, insisting that they return the detailed travel schedules and offering only vague reasons.

Suspicious reporters gave their booklets a closer look and discovered the real reason: An aide in the White House “advance” office that handles the complicated logistics of presidential travel had added an unfortunate rhetorical flourish. The aide had described the chaotic lead-up to a joint press conference between Bush and China’s then-president, Jiang Zemin, as a “Chinese fire drill.”