The Patriots kept busy during the first week of free agency by bargain hunting, so this week strangely could prove more interesting. They remain restricted by limited cap space, but it’s at this time of year, when player asking prices fall, that some of their best acquisition work is done.

Here are the best veteran deals left on the open market.

WR Randall Cobb

A reliable veteran at a position of great value and need? Sign the Patriots up. Even if Cobb, 28, is far from the player he once was, New England can find a use for him.

K Stephen Gostkowski

Gostkowski unquestionably ranks as the best free agent at his position, should share mutual interest in a return and would immediately fill a need. This ought to get done.

P Ryan Allen

Ditto for Allen.

WR Jordy Nelson

Released by the Raiders last week, Nelson’s explosiveness is mostly gone but he offers a strong, physical presence on the outside. A receiver with his savvy and experience would surely be appreciated by Tom Brady.

OT Jermon Bushrod

Bushrod, 34, should come on the cheap after years of logging starts at left tackle in New Orleans and Chicago, then right guard in Miami. He made five fill-in starts at left tackle last season for the Saints.

DT Darius Philon

Los Angeles Chargers defensive tackle Darius Philon (93) celebrates after sacking Cincinnati Bengals quarterback Jeff Driskel, bottom left, on a two-point conversion attempt late in the fourth quarter during an NFL football game Sunday, Dec. 9, 2018, in Carson, Calif. (AP Photo/Mark J. Terrill)

The Patriots have reportedly shown interest in the young run stuffer. He would make a nice pairing with already signed Mike Pennel. Philon earned 13 starts last season with the Chargers.

DL Allen Bailey

Bailey was the rare free-agent visitor who didn’t sign in Foxborough last Thursday. Still, don’t rule out the former Chief who could boost New England’s versatility and depth up front.

EDGE Benson Mayowa

A top-30 edge defender last season by Pro Football Focus grades, Mayowa is a former Cardinal whose already played for four teams. Two years after grabbing a half-dozen sacks in Dallas, he collected four sacks, 38 tackles, 11 QB hits and four passes defensed last year during limited snaps in Arizona.

EDGE Nick Perry

He’s never lived up to his first-round draft status, but Perry could prove effective in a pass-rushing specialist role. The 28-year-old former Packer has yet to play a full 16-game season.

EDGE Justin Houston

Houston won’t command top dollar like the younger free-agent rushers who cashed in last week. However, he’s far from the bargain bin and may be outside New England’s price range given he’s still got a few quality seasons left at a premium position.