Timing always matters in the NFL, even when it comes to free agency.

There are a handful of veterans on the open market who still can help NFL teams, but there has been a long lull in free agency because it’s wise for teams to wait until after June 1 to scoop up those players. Free agents signed after June 1 do not count against next year’s compensatory draft picks.

Of course, the players still available are highly flawed (or else they would have been signed when free agency opened in March), but the New England Patriots still have holes in their depth chart that could be filled with some savvy signings.

Check out the five best fits for the Patriots still on the open market:

1. Dustin Keller

Keller tore up his knee during the 2013 preseason for the Miami Dolphins, but if the tight end can get healthy, he would be a huge weapon in the Patriots’ offense. The Patriots haven’t shown much interest in signing another “move” tight end since Aaron Hernandez was arrested and subsequently released by the Patriots last June, but if New England wants to add that chess piece back into the offense, Keller would be a great fit.

Keller is 6-foot-2, 250 pounds and while he might not have the same speed or agility as he did prior to tearing his ACL, MCL and PCL, it’s worth seeing if he still can get open and add some versatility and depth to a weak Patriots tight end corps that features Rob Gronkowski, Michael Hoomanawanui, D.J. Williams and undrafted free agents Justin Jones and Asa Watson.

2. James Anderson

The Patriots’ fourth linebacker currently is a second-year player who couldn’t find the field on defense or special teams as a rookie in 2013 — Steve Beauharnais. The Patriots went into 2013 with the best linebacker depth in the NFL, but now that Brandon Spikes and Dane Fletcher departed in free agency, the team is left with solid starters and no depth.

The Patriots worked out Anderson, who was a starter last season with the Chicago Bears, in May. The Patriots signed linebacker Darius Fleming around the same time, but Fleming was released by the San Francisco 49ers and didn’t count against the compensatory selections — Anderson would have because he was a free agent.

Anderson’s strength is his pass-coverage ability. If the Patriots want to become more versatile and multiple on defense, it would benefit them to add another pass-coverage specialist to go along with second-year pro Jamie Collins.

3. Ronnie Brown

There isn’t a lot of insurance on the Patriots’ roster at running back if Stevan Ridley’s fumbling issues creep up again. If Ridley falters, the Patriots would have to turn to Brandon Bolden, one of the undersized backs (Shane Vereen and James White) or an undrafted free agent (Stephen Houston).

Brown’s best days are behind him, but Bill Belichick typically likes to see if he can get a last gasp out of a veteran running back. Brown worked out for the Patriots in May.

4. Jermichael Finley

Finley, like Keller, is a move-tight end option who’s recovering from a serious injury. Finley suffered a spinal contusion, which threatened his career, last season and underwent neck surgery.

Finley has been cleared, but teams seem hesitant to sign the 27-year-old tight end, who had 25 catches for 300 yards and three touchdowns in six games before hitting injured reserve in 2013. Finley would add a dangerous weapon, but there’s a lot of risk — and liability — that comes with a player who suffered a serious neck injury.

5. Brian Leonard

Leonard might not be as exciting as some of the other options on this list, but if the Patriots are going to utilize a fullback in 2014, then it makes sense to bring in some competition for the incumbent starter, James Develin.

Leonard offers a better rushing and receiving threat than Develin, and he would come with an endorsement from Belichick’s friend Greg Schiano, who coached the running back at Rutgers and with the Tampa Bay Buccaneers.