Sir John Major told the then American President Bill Clinton that Tony Blair would "do fine" as prime minister, just after Mr Blair trounced him in the 1997 general election.
This remark is revealed in documents recently released in the US by the Clinton Presidential Library about the president's dealings with former British Prime Minister Sir John while both were in power in the 1990s.
Hundreds of pages have been disclosed, in response to freedom of information requests from the BBC and others, which illuminate the relationship between the two world leaders.
The records of conversations between the two men show how they sympathised with each other over their difficulties in tackling international and domestic crises.
They discussed challenges from responding to the "devil's brew" of the Bosnian war to handling an "inebriated" Boris Yeltsin, the Russian President.
In a meeting in April 1995, referring to the Bosnian conflict Sir John said: "We have both been very unlucky to have this insoluble problem on our plates."
President Clinton responded: "We are in the same pickle on the economy. We get no credit for having a sound economic plan."
Sir John replied that he had "the same problem" in the UK, and "no one sees the gains" in the economy.
Later in the meeting the president ruminated on the underlying political changes they faced.
"The central problem of our time", he said, is that "the whole idea of progress is being questioned".
He added: "The people are very susceptible to divisive policies. This is seen in the rising opposition to affirmative action, welfare and immigration."
In a phone conversation in May 1995, Sir John told President Clinton that the IRA ceasefire at the time had not given him a popularity boost.
"For most people here, Ireland is just another island," explained the British prime minister.
"They don't really care what happens elsewhere in the world."
The president sympathised, tell the prime minister: "I know how you feel".
In July 1995, the prime minister commiserated with the president over the continuing inquiries the latter faced relating to an alleged property development scandal.
"I sympathize with you about the Whitewater stuff. I'm sorry it keeps coming up. You don't need that sort of rubbish," he told President Clinton.
The two compared their electoral position. Sir John told President Clinton in 1995 that Labour's big polling lead was "ephemeral" and he expected "a massive return of voters", but he needed to "play it long" and go the full five year period before holding an election.
Sir John went on to lose the 1997 general election in a Labour landslide.
The pair also discussed the stresses of leadership. In a 1996 call, the PM told the president he felt better after a holiday in France and a few days watching cricket. President Clinton replied "I think we don't realise how mentally tired we get", and Sir John responded "I absolutely agree".
Sir John clearly tried hard to build up their personal relationship, particularly given the initial anger in the Clinton team over earlier Conservative Party support for the incumbent Republican president he ousted, George H W Bush.
Soon after Bill Clinton was elected, the prime minister gave him a present which seemed to particularly please him. It was a tie in the colours of University College, Oxford, which the president had attended as a postgraduate student. On a White House memo informing President Clinton of the gift's arrival, in what appears to be his handwriting there is written "I want the tie!".
This correspondence also illustrates an apparent difference between US and UK policies on disclosing records.
The president's letter of thanks for the tie ("Its colors bring back some of the happiest memories of my time spent in your country") has been published by the Clinton Presidential Library. But in the UK's National Archives, where some material relating to the initial phase of their joint time in office has been released, this letter is omitted from the public file, instead listed as "temporarily retained".
The two men clearly got friendlier over time, and the relationship appears cordial and constructive. But it doesn't exhibit the relaxed bonhomie and banter of the much closer friendship between President Clinton and Sir John's successor, Tony Blair.
- You can follow Martin Rosenbaum on Twitter as @rosenbaum6