One he would be delighted to shed; he would not be heartbroken to keep the other.

MONTREAL -- Jacques Demers has the distinction of holding a pair of labels that begin "most recent coach to…"

Demers coached the Montreal Canadiens to their 24th and most recent championship, winning a five-game 1993 Stanley Cup Final against the Los Angeles Kings.

"I can't wait for the day that the Canadiens win another so I'm not referred to as the last coach in Montreal to win the Cup," he said with a laugh from Hallendale, Fla.

It was three years earlier that Demers was the last Detroit Red Wings coach to not bring his team into the Stanley Cup Playoffs, the 1989-90 edition finishing fifth and last in the Norris Division.

Each of the 24 seasons that have followed that early exit have seen the Red Wings qualify for the postseason, during which they have won the Stanley Cup four times and advanced to the Final twice more.

The Red Wings traveled to Montreal to face the Canadiens on Tuesday (7:30 p.m. ET; FS-D, RDS, SNE, NHL.TV) following their nail-biting 3-2 home-ice win Monday against the Buffalo Sabres. Detroit is tied in points with the Philadelphia Flyers in a ferocious battle for the final wild card into the playoffs from the Eastern Conference.

The Flyers, who defeated the Winnipeg Jets 3-2 in overtime Monday, have seven games left to play, one more than Detroit. The New York Islanders are two points up on the Flyers and Red Wings with eight to play.

In the standings, Philadelphia holds the lead because of that game in hand.

To put the Red Wings' run in perspective, with their 24-season streak now on dangerously thin ice: Nine players on Detroit's current 23-man roster were not alive the last time there wasn't a winged-wheel jersey in the postseason.

"It's an unbelievable record," Demers said in reflection. "It's such a great organization. I was glad to be part of it, starting from scratch with the worst team in hockey, bringing it up to a good point. You never want it to stop."

A good point, indeed.

In 19 seasons, from 1966-67 through 1985-86, the Red Wings qualified for the playoffs four times, twice bounced in the first round, twice losing in the Norris Division Semifinals.

The 1985-86 team finished last in the League, its 40-point record of 17-57-6 under coaches Harry Neale and Brad Park 14 points less than the second-to-last Los Angeles Kings.

In 1985-86, Demers was taking his St. Louis Blues to the Western Conference Final against the Calgary Flames, who would win the seven-game series before losing a five-game Stanley Cup Final to the Canadiens.

The coach piqued the interest of Red Wings owner Mike Ilitch, who was impressed with Demers' ability to squeeze the best, and even a little more, out of his players.

Demers was without a contract for 1986-87, though the Blues swore they had signed him to an extension through 1989 and claimed Detroit had tampered to coax him to leave, a charge dismissed by then-NHL president John Ziegler.

Demers' five-year, $1.1 million contract with the Red Wings, including a $100,000 signing bonus, made him the richest coach in hockey at the time and the organization's 17th coach in 18 seasons.

"I remember having dinner with Mr. and Mrs. Ilitch and (then-general manager) Jim Devellano the night before our first game," Demers said. "I was asked to improve the team 50 percent and I said, 'Mr. Ilitch, that would be 60 points. That's not good enough. We have to make the playoffs and we have to think that way.' I wanted to win right away.

"A lot of people said to me, 'You're nuts, your Blues just lost the seventh game of the conference final against Calgary and you could go to the Final the next season.' But I had my [reasons] for leaving."

The lagging contract discussion likely was atop his list.

In Detroit, Demers got instant results and a trip to the conference final, the Red Wings' 78 points nearly doubling what they had earned the previous season. He won the NHL's Jack Adams Award as the League's top coach for the dramatic turnaround.

Demers proved hugely popular with his players and the team's long-suffering fans, even taking the players' wives out to lunch to thank them for "all the little things they do to help."

The coach knew his strengths and, just as importantly, his limitations.

"I'm not an X's and O's guy," he said. "I knew that and I told the players that. But I told them, 'I can give you leadership, communication and have everybody work together and play as a team and succeed together.' A coach is a salesman. I sold it to the team, I sold it to my captain, Steve Yzerman, and we went from there. Obviously, we did well."

Demers then led the Red Wings to the 1988 conference final, again winning the Jack Adams Award, and the 1989 Norris Semifinals before missing the playoffs in 1989-90. It was after that exit that Ilitch stunned hockey by firing Demers with three years remaining on a contract the owner had extended, incoming coach Bryan Murray beginning Detroit's run of 24 straight playoff appearances.

"I was hurt when I was fired, but I never said anything negative about those people," Demers said of Ilitch and Devellano. "I was hurt, but that's life. They paid me everything they owed me. I have the utmost respect for those people."

Demers remains a keen observer of the game from Montreal and from Ottawa, where he sits as a member of Canada's Senate, the country's second chamber of Parliament.

He still has a soft spot in his heart for the Red Wings and thinks kindly of their coach, Jeff Blashill, following the tough decade-long tenure of Mike Babcock.

"I feel bad for Jeff," Demers said of the rookie coach's white-knuckle playoff pursuit. "I remember with the Canadiens or Detroit or St. Louis, I never, ever wanted to miss the playoffs. I'm sure Jeff is a quality coach, he won [the Calder Cup] in the American Hockey League. But some of his players haven't played up to the level they've needed to, and older veterans like Henrik Zetterberg and Pavel Datsyuk … they're among the greatest players in the world, but they can't carry an entire team like they used to."

In Demers' view, a remarkable run like Detroit's will never again be seen because of League parity and the salary cap. The Pittsburgh Penguins are a distant second to the Red Wings' streak with nine consecutive playoff appearances, the Chicago Blackhawks next with seven and the New York Rangers with five.

"Los Angeles wins the Stanley Cup in 2014 and they don't make the playoffs last year," Demers said. "You can't build teams the way you used to.

"If the Red Wings' playoff streak ends this season, that's life. But I'll be honest: I hope it continues forever. I'm prepared to live with the fact that people will keep saying, 'Coach Demers was the last guy not to get Detroit into the playoffs.'"