It has been a little more than a month since the New England Patriots won their fifth Super Bowl title with Bill Belichick as their coach and Tom Brady as their quarterback.

Belichick, despite the “No days off!” chant that he led (or at least attempted to lead) at the team’s victory celebration, has been spotted taking some down time here and there, playing golf at Pebble Beach and nearly being barreled over by LeBron James while sitting courtside.

And oh, by the way, he also has found time to make the Patriots even better.

The champs have done very well since the NFL’s free-agent and trade markets opened Thursday. The Patriots signed cornerback Stephon Gilmore, formerly of the Buffalo Bills, in free agency and they traded for Indianapolis Colts tight end Dwayne Allen, Carolina Panthers defensive end Kony Ealy and New Orleans Saints wide receiver Brandin Cooks.

It isn’t quite time to award the Lombardi Trophy to the Patriots for this coming season. Not yet. But the moves should ensure that the Patriots remain solidly in championship contention throughout the 2017 season, in which Brady will be 40.

Cooks is a very good wideout coming off consecutive 1,100-yard receiving seasons with the Saints. He totaled 17 touchdown catches over that span, and he makes the New England offense even more varied and even more explosive. The cost was not prohibitive, as the Patriots surrendered the final pick of the draft’s opening round, in addition to swapping a third-rounder for a Saints’ fourth-rounder.

The Patriots did not have to include cornerback Malcolm Butler in the Cooks trade – which was thought to be likely at one point – but he’s yet to sign his first-round tender. Butler still could leave via restricted free agency if another team signs him to an offer sheet. If not, the Patriots can pair Butler with Gilmore, a Pro Bowl selection this past season. A good defense gets better, even more so with Ealy on hand to bolster the pass rush a bit. The Patriots are still trying to re-sign free-agent linebacker Dont’a Hightower, who made the game-turning play in the Super Bowl with his sack and strip of Atlanta Falcons quarterback Matt Ryan, but are said to be facing competition from the New York Jets.

Allen’s arrival offsets the free-agent departure of Martellus Bennett. Brady again should have two capable pass-catchers at tight end, assuming that Rob Gronkowski returns for a healthy 2017 season.

The trades have left the Patriots without any picks before the third round of next month’s draft. A Butler deal could change that. Or if Belichick considers it a problem, he easily could remedy it by trading backup quarterback Jimmy Garoppolo to the Cleveland Browns. The Browns possess the first and 12th overall selections in the draft and seem willing to part with the 12th choice as part of a package for Garoppolo.

It is an interesting decision for the Patriots, who could maximize their chances of winning another Brady-led Super Bowl by dealing Garoppolo. But that means trusting that Jacoby Brissett, coming off his rookie season, is ready to be Brady’s primary backup and perhaps his successor-in-waiting.

Either way, the Patriots are primed to enter the 2017 season as a strong, leaguewide Super Bowl favorite.