Tony Blair wanted to do it with John Major but John Major was too coy. William Hague, Michael Howard and Charles Kennedy all wanted to do it with Tony but he said no.
Now David Cameron has his sights on Gordon Brown, and this time it might actually happen.
The question of whether the main party leaders should go head to head in a televised debate comes up at every general election but it has never happened. Peter Mandelson, Gordon Brown's effective second in command, has raised the tantalising prospect that it will happen next year by saying that Mr Brown "wouldn't have a problem" taking on Mr Cameron in a live debate.
Mr Cameron has repeated that he wants a debate, and in today's Independent, the Liberal Democrat leader, Nick Clegg, writes that he is keen, too: "If Gordon Brown believed in the Labour party and his own record, he would be champing at the bit to hold this debate. I'm eager because I want people to know about Liberal Democrat policies."
Traditionally, opposition leaders want to debate and it is the Prime Minister who says no, because he has more to lose by letting himself be seen to come down to his opponents' level.
John Major put the case succinctly after Neil Kinnock accused him of ducking out of a debate in 1992 because he was "frit". "Every party politician that expects to lose tries that trick, and every politician who expects to win says 'no'," Mr Major replied.
The only year when it looked as if a debate might happen was 1997, when Mr Major was so far behind in the polls he had nothing to lose. The Conservatives and Labour both claimed that they were up for a debate, but when party officials met to negotiate the terms, it was quite clear that one side or the other was being awkward. Labour eventually pulled out of the talks, claiming the Conservatives were continually raising petty objections, amid Tory claims of "chickening out".
For the next two elections, there was no prospect of a debate. With his commanding lead, Tony Blair never had the slightest intention of meeting William Hague, Michael Howard or Charles Kennedy in a television studio.
In the US, televised debates have been a feature of the presidential race for the past half a century. One of the main reasons that John Kennedy beat Richard Nixon in 1960 was that he looked much better when they appeared together.
Barack Obama and John McCain had three head-to-head clashes during last year's race, the first of which was watched by an estimated 52.4 million people. They were certainly better for Mr Obama than Mr McCain. As they were leaving the studio after the final confrontation, the older man set off in the wrong direction and had to be called back.
A leaders' debate: Who would chair it?
The 71-year-old Question Time host might seem an obvious choice. But in an unprecedented debate such as this, politicians would be in a stronger position than usual to call the shots, and may complain that Dimbleby would interrupt them.
Gordon Brown would regard Marr as a suitable choice, since they have known each other for 25 years. For the same reasons, the Conservatives might prefer Nick Robinson.
The presenter of The World at One has a gentle style, but knows her stuff. Audiences and politicians might like someone who lets the leaders speak for themselves.
Richard and Judy
On the look out for new opportunities. But would they be up to probing the different parties' policies on taxation and public spending?