Neither wants to leave Ontario without a Stanley Cup.
In telling reporters in Toronto this week that he didn't want to leave the Maple Leafs, the 36-year-old Sundin pointed to the organization's 40-year Cup drought as a major source of motivation to stay and try and get it done.
When told of this, his countryman Alfredsson knew where he was coming from.
"There's no question," said the 34-year-old Ottawa captain. "You think back at the years here, we get a lot of criticism. Losing in Canada is probably the toughest thing you can do. I can only imagine winning in Canada. So you have to take the pros with the cons and I'm always thankful of the opportunity to be on a Canadian team."
"It comes with a lot of pressure but that dream of winning the Stanley Cup in Ottawa kind of makes all the tough times seem not that tough."
Consider the source of that statement. Alfredsson, all of his 11 NHL seasons spent in Ottawa, has long bore the brunt of his team's playoff short-comings. That perception was only strengthened by the image of Buffalo's Jason Pominville skating around him for the overtime goal, which knocked the Senators out of the playoffs in the second round last spring.
Alfredsson, who got skewered by fans on radio call-in shows that night, didn't hide. He stood in the dressing room and answered question after question after question: How does it feel to be the goat? How does it feel coming short again in the playoffs? What's wrong with this team? Will this team ever win? Is it time to blow up this core?
That last question hit a nerve. With the pain of a yet another earlier-than-expected playoff exit still fresh in the wounds, Alfredsson pleaded his case for patience.
"We've done so many good things, we have to keep believing," he said that night of May 13.
Fast forward 11 months later. Alfredsson is back for a 10th consecutive playoff drive. And if his team fails, he'll once again wear the goat horns, be the lightning rod for a market ultra-sensitive to playoff failure.
Other players might have looked for a change of address a long time ago, especially after last spring when he really took it on the chin. Why go through this every year? But Alfredsson said leaving town never once crossed his mind last summer.
"No, and the biggest reason is because I didn't feel like I played to the best of my best capabilities," said Alfredsson. "That's the most frustrating thing, when you know what you can do and you're not doing it. My motivation has always been to try and get better. I think I've had a better year this year. I'm more rested this year compared to last year as well because of the Olympics and everything."
Defenceman Wade Redden has been here almost as long as Alfredsson and lived through that playoff frustration. And he, too, shares Alfredsson's desire to get it done and not give up.
"I've been here 10 years," said the 29-year-old native of Lloydminster, Sask. "I'm a Senator, that's what I am, that's all I know. To leave, that would be tough to start somewhere new. To be on a team that's been trying to win it for so long ... we'd love nothing more than to do it here in Ottawa."