Segura, whose double-fisted forehand and shrewd lobs enhanced the professional circus in the days when it was frowned upon by the tennis establishment, later helped guide Jimmy Connors to his early successes. For the past 21 years he has been tennis director of the La Costa Resort and Spa in California.
The short-term goal is to improve Agassi's ranking from No 21 in the world in order for the Las Vegan to be seeded for the United States Open, which starts on 30 August.
'Andre came to La Costa in April, but he didn't come with the idea of changing from Bollettieri to Pancho Segura,' Segura said yesterday in Washington DC, where Agassi is playing his first tournament since losing to Pete Sampras at Wimbledon. 'He came back a couple of weeks ago and offered me the position of coach, and I took it. We've been working since. We've got five tournaments. This is the first one, and we look forward to the US Open.'
After that, the position will be reviewed. 'Hopefully we can continue,' Segura said. 'I would like to be with him for a couple of years if I could, because I think he can be No 1, although he claims he's getting old already. He's only 23. With me he can mature a little, too. He will learn to play points a little better.
'I worked with Jimmy Connors from when he was 17 and was with him when he won Wimbledon in 1974. He was my prize pupil. After that I never taught anybody. I never went for anybody and they never came to me, because I'm too expensive and also I don't teach anybody that doesn't have any chance of being a champion. In other words, I give one hundred per cent and I don't want anyone who isn't a fair tennis player. They've got to have the fundamentals under control, meaning the strokes, the ingredients of hand and eye co-ordination, balance, plus competitive ability.
'Agassi has everything, almost. Where I'm concerned is that his concentration drifts up and down a little bit, and we have to make sure that doesn't happen and he doesn't play too many loose points.
'He will learn with me to cut down on unforced errors. He will learn to play the open court more, and he's going to do more volleying, too. And he will learn to have the guy beat you, don't beat yourself. It's exciting, because we can perfect what he's got. He's one of the few players in the game who has got equally balanced strokes.'
Was Segura surprised that Agassi hired him, if not startled, as were some observers? 'To a degree, yes, of course I was surprised. To work with a tremendous talent like that is also flattering and an honour, because I consider Andre one of the future great players.'
Is it possible that Agassi's friendship with John McEnroe will come between them? 'I sense he would like to coach Andre, but I think he's more interested in being the Davis Cup captain,' Segura said. 'I think he's one of the great players of all time, but I think subconsciously there might be a conflict of personality or ego with Andre.'
Though Agassi is considered to be the best returner of serve since Connors, Segura sees room for improvement. 'On second serve he's good, but on first serve he's not so good. He doesn't return first serves that good, in my opinion. Not like Connors. He's better than Connors on second serve. He could even be better if he came to the net behind the second serve return once on a while.
'He's got the best return of second serve - some people might say even the first - provided a guy comes to the net. If the guy is at the back on that return of serve, it's not that great. McEnroe was better than that. So was I, so was (Frank) Sedgman, pressing you on second serve return. Second serve return is only good if you can go to the net with it, so you can press the other guy.'
And what about Agassi's improvised tomahawk chop serve? 'At the present time it suits him, but I'm not one hundred per cent for it. . . He loses momentum a little.'
Will he teach him the two-handed forehand? 'No, hell, no. But I wish he could drop-shot like me. I've got the best drop-shot in the world, without bragging. And I've got a great lob, too.'
Andre Agassi has been selected for the US Davis Cup squad that meets the Bahamas in September. His team-mates are Malivai Washington, Patrick McEnroe and Richey Reneberg.