Going into an uncapped season, the Jets could be opening the checkbook to re-sign players without breaking any NFL rules. But Jets general manager Mike Tannenbaum seems to be doing just the opposite.

Productive veterans like RB Thomas Jones and K Jay Feely were asked to take pay cuts, and they aren’t the only ones who have been affected. Running back Leon Washington, who is trying to renegotiate his contract, isn’t attending the voluntary workouts at Florham Park coming off a serious compound fracture. Even a veteran like FB Tony Richardson wasn’t secured at the start of free agency.

The fact that Feely will play for Arizona because the Jets wanted to save about $300,000 on his approximately $1.5 million salary is interesting. (Some Jets fans might have a better word to describe that, but this is a family blog.) The team doesn’t need that money to sign someone else, it doesn’t have a proven kicker on the roster and it will have to spend just as much to procure a name-brand replacement.

Looking at the Thomas Jones situation, the Jets parted ways with Jones after his 1,402-yard, 4.2 yards-per-carry season to sign San Diego’s LaDainian Tomlinson, who had 730 yards and averaged 3.3 yards per carry. You could certainly argue that the Jets didn’t want to pay Jones’ bonus, but the team didn’t save money in going for a likely future Hall of Famer. Two years ago, the Jets spent to get Brett Favre, and the one-year experiment didn’t end very well.

On Thursday, Bart Scott said that the Jets need to build toward this season, because what comes after is such a question mark.

“There’s a sense of urgency because we have a good team, we know we have a good team and we don’t know how long we’re going to keep these players together,” Scott said.

So why not secure proven players who helped the team reach the AFC Championship game? The fact that the Jets aren’t doing that, but are instead using a sum as relatively insignificant as $300,000 as a sticking point in a win-now year, is certainly curious.

Especially when you consider that less productive players, such as DE Vernon Gholston -- a third-year player Mel Kiper Jr. described as a bust -- will take up considerably more of the Jets budget.

Tannenbaum has made some smart moves, trading up for Mark Sanchez and Shonn Greene, but he has let contributors like Chris Baker and Pete Kendall slip away for far less than those rookies would see. Sometimes an unknown player can seem pretty tempting, but it may not be a sound strategy to overlook the player already in the system.

UPDATE: Adam Schefter reports that the Jets will host Neil Rackers, the Cardinals free agent kicker, on Tuesday.