For Svehla, the decisive break came in the 1991-92 season. It was his first time to play on Czechoslovakia's national team. With them he won the bronze at the Albertville Olympics and later at the World Championship, where he was named best defenceman. With the Dukla Trencin club he took the championship title, and at the end of the season he won the Golden Stick Award as the top player in the country. From there his career took off.
He wasn't necessarily unknown before, and after leaving his native town of Martin, Slovakia, his road to the top wasn't all smooth. It was just that his success came all at once. Back in 1987, he'd won silver in the European Junior Championship. However, as soon as he arrived in nearby Trencin, he immediately became a fixture on the back lines of his team. Only in his third season, playing next to Milos Holan and with the highly productive offense of Zigmund Palffy, Robert Petrovicky and Branislav Janos, did he draw attention to himself with some pretty high numbers.
In the summer of 1992, the Calgary Flames drafted Svehla. Svehla stayed in Malmo for three years. He was one of their most productive defencemen and at the same time had an average of 99 penalty minutes per season, with 127 in 1993-94. Although he hadn't played a single match in the NHL, the Calgary Flames in the meantime traded him to Florida together with Swede Magnus Svensson. Toward the end of the 1994-95 season, he managed to play five games for the Panthers. No one could have imagined how quickly he would become their leading defenceman.
At the age of 25 he was still considered a rookie, but on the ice he didn't look at all like the typical nervous greenhorn. Instead, he became one of the team's workhorses. Former coach Doug MacLean called him the toughest player to come into his hands during his three years with the Panthers. Svehla could get respect in front of the net. As an experienced skater, he cleared space at the net and attacked near the boards just as strongly. But he wasn't getting about 30 minutes of ice time per game for those reasons alone. He brought the Panthers perspective and a talent for clever passing and hard shooting.
In the spring of 1996 the Panthers quite unexpectedly progressed to the Stanley Cup finals. With 57 points, Svehla had an excellent season behind him. He also did quite well in the playoffs, where he and Terry Carkner allowed Mario Lemieux and Jaromir Jagr only two goals in the best-of-seven finals of the Eastern Conference against Pittsburgh.
After representing Slovakia at the 1996 World Cup, Svehla went on to score a career-high 13 goals in 1996-97, collected 45 points and lined up for the NHL All-Star Game. Svehla went on to play eight seasons in Florida and represented his homeland at the 1998 Winter Olympics in Nagano and later that spring at the World Championships before being acquired by the Toronto Maple Leafs in the summer of 2002.
One of the more durable players in the league, Svehla played his fourth consecutive season without missing a game in 2002-03 and was a member of Slovakia's silver medal team at the 2003 World Championsihps.
