Smith's star is the 16-year-old Essex gymnast Annika Reeder, who in 1994 became the youngest-ever gold medallist at the Commonwealth Games. Today she hopes to add a European medal to her hoard, before going on to the greatest challenge of her young life in Atlanta. "I'm really looking forward to Atlanta," she said after training. "But I expect I'll be very nervous when I get there."
Nerves are the gymnast's greatest enemy. In a sport where a fraction of an inch can make the difference between a medal and ignominious failure, a trembling hand or unsure foot is a perilous handicap. Smith is constantly fighting to protect his girls from their own fears. "Psychology is a big part of what I do," he said. "The first thing that I try to do is to make sure that they are happy and well prepared."
When the girls are starting out this means plenty of soft matting and physical support from the coach in difficult manoeuvres. Nothing promotes confidence like the knowledge that you won't get hurt if you get something wrong. "When they are happy with what they are doing," Smith explained, "they no longer need the physical support."
But the need for psychological care will always remain, and that was one of Smith's main functions on Wednesday night. As the gymnasts moved around the four areas of competition in the Arena, the floor, the asymmetric bars, the vault and the beam, Smith followed, dispensing advice, casting a critical eye over technique, but above all boosting confidence and morale.
Reeder clearly thrives on his counsel. "He's just a really good coach," she said. "He's helped me an enormous amount, and that is why I have stayed with him." Even though Reeder is only 16, the pair have been working together for more than a decade. "He's been with me since I was four."
Smith can still remember when he first came across Reeder. "She was one of a group of four young gymnasts," he recalled. "Each of them had great potential, but for one reason or another the other three dropped out of the sport. Annika has kept on." And in so doing she has developed a physique and mentality that is ideally suited to her strongest discipline, the floor exercises.
She is slight, as so many of her rivals are, but she is also strong, with broad shoulders and well-developed musculature. "Her physique is just right," Smith said. "She also has very good fast-twitch muscle response, which generates a lot of power - that gives her a head start. And she is a dancer; she interprets her music very well."
Reeder's floor routine is carefully crafted to show off both her athleticism and her rhythmic grace. It opens with two tumbling sequences across the diagonal of the floor, then moves into a slower phase of dainty arm movements, interspersed with balletic leaps and swallow-dives. Then more flips and somersaults before a Torvill and Dean-style dying swan finish pose. "I was pleased with that," she said afterwards. "I did it all clean, and that is the important thing."
It was more than many of her rivals could achieve. All evening the vast barn of the arena echoed with shrill cries of dismay as minute Bulgarians and powerful Danes bounced off the mats in unseemly tangles of limbs.
Others, though, were awesomely composed. The world champion, Lilia Podkopayeva of the Ukraine, drew gasps with her opening forward double somersault, and finished her floor routine to a great volley of applause from her fellow competitors. And Svetlana Korkhina, of Russia, known on the circuit as "Princess Di" for her height, hairstyle, make-up and moods, was similarly impressive.
But Reeder was not intimidated. She knows that she is capable of challenging the very best on the floor: she was in the top five at the French International meeting in March, and - encouragingly for Atlanta - in the top 10 at the world champ- ionships in Puerto Rico. And despite the importance of this weekend's event, she has one or two moves that are being saved up for the Olympics.
But they will only be brought into the routine when she is ready for them. "In gymnastics," Smith explained, "you work with the level of difficulty. If you are working at the very limits of the gymnast's ability, the added stress of competition can make things very difficult. So there are things in the pipeline for Atlanta that we are working up to now. Once everything is in place, and properly prepared, we will introduce them."
And the Olympic judges will decide whether or not she was really ready.