It’s not who the New England Patriots picked up, it’s who they kept.

The Patriots decided to trade neither backup quarterback Jimmy Garoppolo nor defensive back Malcolm Butler over the three days of the NFL draft. Both had been the subject of active trade talks, with New Orleans pursuing Butler and Cleveland going after Garoppolo even up until the second day.

Garoppolo is a former third-round pick out of Eastern Illinois who performed well before he was injured as Tom Brady’s backup during the Deflategate suspension. When Garoppolo’s contract expires after the 2017 season, Coach Bill Belichick will have to decide whether to overpay him to smooth the transition for a time Brady is injured or retires.

Butler was the hero of New England’s Super Bowl victory in 2015 over the Seattle Seahawks, intercepting Russell Wilson at the goal line in the final minute. He can become a free agent after this season, and the Patriots talked with New Orleans about a deal that would have brought a first-round draft pick in return.

The Saints refused to give up their pick, No. 11 overall. They also had the No. 32 pick they obtained from New England for receiver Brandin Cooks, but no deal could be worked out.

But that didn’t mean Belichick wasn’t in a trading mood.

The Patriots used their top picks as trade bait, landing not only Cooks from the Saints but also pass-rusher Kony Ealy from Carolina for a second-rounder. They also gave up draft picks for tight end Dwayne Allen and running back Mike Gillislee.

On Saturday, New England shipped another pick (No. 183 overall) to Kansas City to get tight end James O’Shaughnessy and the No. 216 pick. They traded that and a seventh-rounder to take tackle Conor McDermott from UCLA.

Belichick made four trades over the three days. The Patriots entered the weekend with seven picks and wound up selecting just four players.

The Patriots already had forfeited their fourth-round pick – with $1 million and a 2016 first-rounder – in the ball deflation scheme known as Deflategate. After that pick – the 118th overall – was skipped, the Philadelphia Eagles picked North Carolina receiver Mack Hollins.

It’s not the first time the NFL has penalized the Patriots for cheating. After they were docked a first-rounder in the 2008 draft for the Spygate videotaping scandal, the New York Giants moved into their slot and took Miami safety Kenny Phillips.

And the spot for the 2016 first-rounder they lost in Deflategate was inherited by Arizona, which used it to take Mississippi defensive tackle Robert Nkemdiche.

In addition to the trade for Ealy, the Patriots picked up a pair of pass-rushers in the draft: Youngstown State defensive end Derek Rivers in the third round and Arkansas defensive end Deatrich Wise Jr. in the fourth.

They also added a pair of offensive linemen: Antonio Garcia from Troy and McDermott.

Among the undrafted free agents the Patriots signed following the draft were twins Jacob Hollister of Wyoming (tight end) and Cody Hollister of Arkansas (wide receiver).

Other free-agent signings – according to newspaper reports, player tweets or agent tweets – were defensive tackle Josh Augusta of Missouri; linebacker Harvey Langi of Brigham Young; safety Jason Thompson of Utah; guard Jason King of Purdue; cornerback Kenny Moore of Valdosta State; defensive end Corey Vereen of Tennessee; and safety David Jones of Richmond.

After the draft, the Patriots had 20 spots to fill on their 90-man roster.