He wants to be thought of as more than a mere dealmaker, and he is increasingly exasperated by the outside world's insistence on harking back to Storehouse's many management changes in recent years.
'How long do you think it will take before the press stops referring to the management changes at Storehouse?' he asked plaintively. A couple of years, I hazarded.
No surprise, then, that many of the slides in the latest presentation Edelman made to the analysts featured the word STABILITY in large letters.
As for his personal reputation, Edelman, aged 43, is irked by the remark of Archie Norman, chief executive of Asda Group, that he had 'got the deals bug', implying some uncontrollable compulsion.
'During my two years at Grand Metropolitan I was in operational management jobs,' he pointed out, 'and in my two and a half years at Carlton Communications I was nothing to do with strategy. In my last three years at Ladbroke Group I was running Texas Homecare. I was also responsible for strategy there, but we didn't make any acquisitions during that period of time. We only did so in my first couple of years at Ladbroke. So one has got to be very careful about pigeon-holing people.'
Lest there be any lingering misunderstanding, his shareholders may be relieved to hear that Edelman has in effect ruled out any takeovers for at least the next couple of years, until he has got Storehouse sorted out and running the way he wants it.
'We are not looking to make acquisitions or expand the group,' he said. 'We have enough to do for a number of years. But when we have finished the present phase, we have got to sit back and look again. But we know the effort, the pitfalls and the trauma that go into acquisitions.'
Storehouse has already encountered plenty of pitfalls and trauma as it has struggled to recover from 1991's pounds 17.5m loss. But on Thursday Edelman unveiled a jump in profits from pounds 15.2m to pounds 62.4m, giving him a solid platform from which to go forward.
It is perhaps a sign of Edelman's relatively youthful innocence at the commanding heights of public company life that he appears almost as concerned with the style as the substance of what he is up to. In a few years, when he has some solid achievement under his belt at Storehouse and is getting into his stride as a chief executive, we can look forward to him becoming more content to let his actions speak for themselves.
Yet the one really awkward moment in an otherwise remarkably hitch-free upward career path occurred when he let his true zeal show through.
This was the time he told the board of Ladbroke, including the then chairman and driving force, Cyril Stein, exactly what he thought of their plans for the hotels, betting and DIY stores group and - by implication, at least - what he thought of them.
Edelman said: 'I fundamentally disagreed with the strategy for the group, and some of its practices, so I said my piece and left.'
When I suggested that arguing for changes in strategy must have been difficult when Stein was so dominant, Edelman did not give a direct answer.
Instead, he said: 'When you take on the mantle of a public company director you take on a lot of responsibilities, and I think you've got to discharge those responsibilities in a very professional way. You're not there for some sinecure, but to serve the shareholders, and if you've got something to say about the business you should get up and say it. That's always been my policy.'
Very laudable, but Edelman duly paid the traditional price of such outspokenness: he was invited to seek opportunities elsewhere.
Happily, he had had the foresight to make other arrangements before getting his innermost feelings off his chest. The announcement of his departure from Ladbroke in March 1991 coincided with the news that he had fetched up as right-hand man to Michael Green at Carlton Communications, the media group that now owns the Midlands and London mid-week independent television franchises.
While Edelman's talents and experience undoubtedly qualified him for that demanding job, it did no harm that he and Green both sprang from the entrepreneurial north-west London middle classes that also produced Gerald Ratner, the Saatchi brothers and Martin Sorrell of the WPP advertising group.
Indeed, Sorrell and Green preceded Edelman at Haberdashers' Aske's school in Elstree, Hertfordshire. Sorrell recently became a non-executive director of Storehouse.
Edelman lives with his wife and two teenage sons in Northwood, Middlesex, a few miles from where he was brought up. His father, an accountant, died when he was young. 'That sharpens you up,' was all he would say about what must have been a difficult part of his life.
He was brought up among other accountants in the family. The culture seeped into his veins: at the age of 16 or 17 he decided he wanted to go into business.
So from Haberdasher's he went to the University of Manchester Institute of Science and Technology, where the professor of marketing was none other than Roland Smith, later to become the scourge of Lonrho's Tiny Rowland and now the chairman of the quoted parent company of Manchester United Football Club.
From UMIST he went to what amounted to post-graduate courses at IBM and Xerox. With the basics of business under his belt, he decided he needed a proper grounding in banking, so he went off to the British end of Bank of America.
There Edelman had his first real taste of strategic planning and became the bank's financial controller for the UK and managing director of its leasing and consumer finance offshoot.
It was at his next port of call, the Grand Metropolitan drinks and catering group, that Edelman began to get near enough to the top of the greasy pole to conceive the desire to run a public company. There, too, he worked for Sir Allen Sheppard, the first in what turned out for Edelman to be a trio of the strongest personalities in British business. He imbibed Sir Allen's no-nonsense approach to reaching the heart of a problem and getting the job done.
After that, Edelman went on to Ladbroke, where he was struck by Stein's 'sheer passion for the businesses. He lived and breathed them.'
Even Carlton, where outsiders reckon Edelman was never totally comfortable, was part of his learning experience.
'Michael Green taught me the importance of cash and cash flow,' he testifies.
At 43, Edelman has far to go. The shrewder analysts doubt whether he will end his days at Storehouse. And when he does, he is likely to leave it in a very different shape from the bedraggled company he inherited last summer.
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