Bill Clinton Was George W. Bush's Secret White House Whisperer

George W. Bush was known – and often criticized – for being insular during his eight years in the White House, but he made regular calls to a surprising adviser during his second term: his predecessor.

Bill Clinton revealed on Monday that the second President Bush picked his brain twice a year for 30-45 minutes, in wide-ranging conversations that no doubt set the stage for the surprising, "brother-from-another-mother" relationship that the two ex-presidents now share.

Bush would call Clinton "just to talk," during his last four years in the White House, the Democrat said in a joint event at the Newseum in Washington.

It meant a lot to me. We never talked about it. We never talked about it in public. We talked about everything in the wide world. He asked my opinion – about half the time he disagreed with it."

It wasn't clear if Bush wanted Clinton to reveal their private talks at the event, which was held to announce the launch of the Presidential Leadership Scholars program.The initiative is a partnership between the presidential centers of Clinton, Lyndon B.Johnson and the two Bushes.

Much like Clinton and former President George H. W. Bush, Clinton and the younger Bush have become close and appeared frequently together in the years since President Obama took office. Clinton joked, as he has before, that he had become "the designated black sheep of the Bush brood."

They spent much of the event praising each other, somewhat convincingly.

Clinton put a positive spin on Bush's well-known distaste for "nuance," saying that when he decided "what he thought was right, he went for it."

"The truth is," Clinton added, "sometimes clarity is required."

For his part, Bush said Clinton was "an awesome communicator."

Clinton, in a vaguely backhanded compliment, also praised Bush for constantly exceeding expectations:

You always want to be underestimated by your adversaries. He consistently benefitted by being underestimated. And so did I, for totally different reasons."

A running theme of the event was the gushing that both men lavished on Bush's father, who sent along a note in his absence. The younger Bush repeatedly plugged his forthcoming book, 41, leading Clinton to quip: "I learned a lot from him and I’m not making any money off of it."

The two men also mused about people begging them now for more selfies than handshakes – "At least they're still asking," Bush joked.

And with Chelsea Clinton due to have her first child soon, Bush offered Clinton some advice on being a grandfather: "Get ready to be like the lowest person in the pecking order in your family," he said to laughs.

Clinton and Bush could find themselves on opposing sides of the campaign trail again in a couple of years, but in perhaps the morning's most surprising development, the words "Hillary" or "Jeb" were never mentioned.