Even the GM whose team won the Stanley Cup -- this year it's Jim Rutherford of the Pittsburgh Penguins -- can't sit idly by when all of his counterparts are busy trying to gain an edge anywhere they can.

The Stanley Cup is awarded in June, and by early July general managers across the NHL have done most of the heavy lifting to remake their team so it will have a chance to potentially win it next year. It's an annual summer rite of passage.

The good GMs base their offseason moves on the recognition of certain League-wide trends (currently, speed and three lines of scoring depth) and where they went wrong with their roster last season.

Here are five teams from the Western Conference who, at least on paper, appear to have helped themselves the most so far this offseason (list in alphabetical order):

Video: STL@DAL, Gm5: Goligoski goes top-shelf to even score

ARIZONA COYOTES

Key moves: Signing defenseman Alex Goligoski (5 years, $23.375 million) and forward Jamie McGinn (3 years, $10 million); re-signing defenseman Kevin Connauton (2 years, $2 million).

The Coyotes added the potential of 20 or more goals with McGinn and a versatile threat on the blue line with Goligoski, who should contribute on the power play. With Oliver Ekman-Larsson, Goligoski, Connauton and Klas Dahlbeck, they should have the left side of their defense covered. Michael Stone, Connor Murphy and Zbynek Michalek could make up the right side. McGinn could slide into the top-six forward group or add scoring depth on a third line.

No. 1 on the to-do list: Re-sign longtime captain Shane Doan, who is an unrestricted free agent.

Video: SJS@STL, Gm1: Elliott robs Pavelski to preserve lead

CALGARY FLAMES

Key moves: Acquiring goaltender Brian Elliott in a trade with the St. Louis Blues; signing forward Troy Brouwer (4 years, $18 million) and goaltender Chad Johnson (1 year, $1.7 million); taking forward Matthew Tkachuk with the No. 6 pick in the 2016 NHL Draft; acquiring forward Alex Chiasson in a trade with Ottawa Senators and signing him (1-year, $800,000).

The Flames had the worst save percentage in the NHL last season (.898). Elliott and Johnson were in the top 14 among goalies with 40 or more appearances: Elliott was first (.930) and Johnson was 14th (.920). Brouwer adds power and experience to what was a lighter and younger group of forwards. Chiasson could add scoring depth; he scored six goals in seven games playing for Flames coach Glen Gulutzan with the Dallas Stars during the 2012-13 season.

No. 1 on the to-do list: Re-sign restricted free agent forwards Johnny Gaudreau and Sean Monahan. The Flames have about $14.9 million in NHL salary cap space, according to General Fanager.

Video: Lucic signs seven-year deal in Edmonton

EDMONTON OILERS

Key moves: Signing foward Milan Lucic (7 years, $42 million); acquiring defenseman Adam Larsson in a trade from the New Jersey Devils (for forward Taylor Hall); selecting forward Jesse Puljujarvi with the No. 4 pick in the draft.

Oilers GM Peter Chiarelli made the controversial decision to trade Hall for Larsson, who hasn't yet shown the multidimensional skill set New Jersey thought it was getting when it made him the No. 4 pick in the 2011 NHL Draft. Larsson does give the Oilers a right-handed defenseman they needed badly. He's 24, and defenseman typically take longer to develop, so Edmonton could be getting him at the ideal time. Chiarelli felt he could replace Hall because he drafted Puljujarvi and knew he was going to sign Lucic when the free-agent market opened July 1. Lucic won the Stanley Cup with Chiarelli in Boston five years ago and returned to the Stanley Cup Final in 2013. He will be expected to play a big role in the culture change Chiarelli and coach Todd McLellan are trying to foster. Puljujarvi joins a young core already in place.

No. 1 on the to-do list: Nothing pressing. The Oilers need to see how their revamped roster works before tinkering more.

Video: Top Moment: Staal Scores One-Handed

MINNESOTA WILD

Key moves: Signing forwards Eric Staal (3 years, $10.5 million) and Chris Stewart (2 years, $2.3 million); buying out forward Thomas Vanek, who had one year remaining on a three-year contract.

The Wild are counting on Staal having a lot left in the tank because they need him to be a center on one of their top two lines (center depth was a problem last season). Staal is coming off of his worst offensive season since he was a rookie in 2003-04; he had 13 goals and 39 points in 83 games with the Carolina Hurricanes and New York Rangers. The 32-year-old said the Wild give him a chance to get back to being close to the player he once was. He'll be a success if he scores 20 goals, has 60 points, and continues to be the positive possession-driver he has been. Stewart could provide depth scoring. Buying out Vanek saved $5 million on the salary cap this season.

No. 1 on the to-do list: Re-sign defenseman Matt Dumba, who is a restricted free agent.

Video: Reaction to the Subban/Weber trade

NASHVILLE PREDATORS

Key moves: Acquiring defenseman P.K. Subban in a trade from the Montreal Canadiens (for defenseman Shea Weber); re-signing forward Filip Forsberg (6 years, $36 million).

Although it cost them their captain and an excellent defenseman, the Predators acquired the most talented player who changed teams this offseason: Subban (27 years old) is younger than Weber (30), faster, louder and more entertaining. He's a possession-driver who is slightly more effective than Weber in terms of production. Subban averaged 0.670 points per game in the past five seasons (238 points in 355 games), Weber averaged 0.634 (229 points in 361 games). Re-signing Forsberg proves the Predators are intent on having a solid core of skaters in their 20s, which potentially could turn into a championship core before any of them hit their 30s. Forsberg, Subban, Ryan Johansen, Roman Josi, Craig Smith, Colin Wilson, Ryan Ellis and Mattias Ekholm are between 21 and 27 years old. James Neal will be 29 on Sept. 3.

No. 1 on the to-do list: Sign Johansen to a contract extension so he's all but guaranteed to be part of the core for the foreseeable future. He has one year left on his contract.