This time may be trickier, as Bergevin and his staff go into Sunday's draft holding the 25th overall pick. However, having six picks in the first three rounds could make it interesting.
"Last year we only had two picks before ours and we had a good idea of what we were going to do," said Bergevin, who selected forward Alex Galchenyuk. "This year, it's completely different."
And this time there is unexpected extra pressure on Bergevin in the form of centre Vincent Lecavalier.
Montreal fans are pushing hard for the Canadiens to sign Lecavalier, who entered the unrestricted free agent market on Thursday when the Tampa Bay Lightning announced they were buying out 33-year-old's hefty contract.
The Canadiens have not had a French-Canadian star in many years, and Lecavalier would fit that bill. They also want to get bigger up front, and Lecavalier is six-foot-four. And, with 20 players signed and $9 million in salary cap space open, they should be able to afford him.
Even Mathieu Darche, a former Canadien and Lightning, urged Bergevin on his blog for RDS to sign the slick centre who scored 52 goals in 2006-07.
The temptation to make a play for his former teammate in Tampa would have to be enormous, even if it seems to go against Bergevin's philosophy.
"To me, free agency is a tool, but it's not a way to make your team a top team," he said. "It's overplayed. You have to be really careful with free agency."
He does not rule out making a deal to move up in the draft, however. The Canadiens have three second round picks, including the 34th and 36th overall from previous deals, as well as their own 55th pick. They also draft 71st and 86th overall in the third round.
"I can say we're always looking to improve our position, but there's a price to pay," he said.
"You don't build a team through free agency or trades, you build it through the draft. And you need to be patient with these guys. Look at the teams that have success, like Chicago. The core of their players, most of them came through the draft. And it took years for them to become the elite team they are now. It's not a secret recipe, how to build a hockey team."
He gave no indication on what sort of players he and scouting director Trevor Timmins are looking for.
After his smaller-than-average team was eliminated in the first round of playoffs by Ottawa, he said he would like more "balance" between big and small players. So they may look for some bigger bodies.
The organization is also thin on goalies, having not drafted one since they took Petteri Simla 211th overall in 2009. They have selected only two since they got Carey Price fifth overall in 2005.
So they may be tempted by Halifax Mooseheads goalie Zach Fucale.
There are a handful of other prospects from Quebec who may be available if that is a consideration, including defenceman Samuel Morin and forwards Laurent Dauphin, Anthony Mantha and perhaps Frederik Gauthier.
The flashy Jonathan Drouin, expected to go in the top five, is likely out of their reach. Bergevin said it would take more than offering a first and second round pick to move up that high.
"It's not just to draft the players available, but to draft the players you like," he said. "If you can move up and get that player, and it comes at a price you feel is not too steep, then I will do that."
What he has to offer is other draft picks.
"Especially in the early second (round)," he said. "The 34th and 36th. Those are really good picks. They're appealing picks."
Montreal has its best collection of picks since it had five in the top 73 in 2007. That year, they got Ryan McDonagh (now a New York Ranger) 12th, Max Pacioretty 22nd, Norris Trophy winner P.K. Subban 43rd and defenceman Yannick Weber 73rd.