There’s mixed news for the New Orleans Saints as the NFL prepares for its annual winter/spring shopping spree known as veteran free agency.

The good news: The Saints don’t have nealy as many of their top players hitting the market as they did a year ago.

On the flip side, they won’t have a lot of salary-cap space to sign players who could come in and help turn things around after a 7-9 season snapped the franchise record-tying three-year playoff run.

The Saints had to make a series of moves to get close to the salary cap of $123 million for this season, which kicks in with the start of the new league year at 3 p.m. Tuesday.

The Saints were believed to be about $3 million over the cap before making three moves Saturday, which means that they have to clear a lot more room before they can begin to re-sign their unrestricted free agents — or some from other teams.

But unlike last year, when they gave quarterback Drew Brees the franchise tag and had to deal with guard Carl Nicks, receivers Marques Colston and Robert Meachem, cornerback Tracy Porter and linebacker Jo-Lonn Dunbar, the Saints have a much shorter list to worry about.

Their top priority, of course, is two-time Pro Bowl left tackle Jermon Bushrod, who figures to be a hot commodity on the open market because of the position he plays.

While each potential free agent is evaluated separately, the Saints have set a precedent for offensive linemen in allowing Nicks, a first-team All-Pro in 2011, and centers Jeff Faine and Jonathan Goodwin to walk rather than overpay for their services.

Bushrod just completed a two-year, $10 million contract that he signed in 2011, which means he’ll be looking for a longer deal with a matching pay increase after playing in the past two Pro Bowls.

The Saints’ other UFAs are linebackers Jonathan Casillas, Scott Shanle and Ramon Humber; quarterback Chase Daniel; defensive tackle Sedrick Ellis; receivers Devery Henderson and Courtney Roby; cornerback Elbert Mack; defensive end Turk McBride; and tackle William Robinson. Agents for those players were allowed to talk to the Saints and other potential suitors during a three-day negotiating period that began at 11 p.m. Friday.

The Saints got three of their four restricted free agents taken care of Saturday morning when defensive end-turned-linebacker Junior Galette agreed to a three-year contract. General Manager Mickey Loomis later confirmed that center Brian de la Puente and running back Chris Ivory were given one-year tender offers.

De la Puente and Ivory, who’ll each receive $2.023 million in base salary, can still negotiate with other teams. If they were to get an offer, the Saints would have an opportunity to match it and retain the player or receive a second-round draft pick as compensation.

Long snapper Justin Drescher is the Saints’ only remaining restricted free agent, but the Saints likely won’t tender him and will try to re-sign him to a cheaper deal than the lowest tender of $1.323 million.

Galette, a 6-foot-2, 258-pounder, has 9.5 sacks for his three-year career in 32 games with two starts. He has 26 tackles on defense and 15 more on special teams.

De la Puente, a former practice squad player who made the active roster in 2011 and started 12 games that year after veteran Olin Kreutz abruptly retired, started all 16 games last season.

Ivory led the Saints in rushing with 716 yards in 2010 after making the roster as an undrafted free agent; he has career totals of 1,307 yards and eight TDs in just 24 games. He’s averaged 5.1 yards per carry for his career.

The Saints reduced their salary-cap number considerably in the past few weeks by restructuring the contracts of six players — Colston, guards Jahri Evans and Ben Grubbs, linebackers Curtis Lofton and David Hawthorne and defensive tackle Brodrick Bunkley. The team also reportedly asked defensive end Will Smith and linebacker Jonathan Vilma to reduce their deals in order to return to the team.

Smith, Vilma and strong safety Roman Harper account for about $30.2 million in cap space — nearly one-fourth of what the team will have available to them Tuesday afternoon. Smith carries a cap figure of $14.5 million, while Vilma and Harper have cap hits of $8.6 million and $7.1 million.

If they get significant cap relief from Smith and Vilma, either from pay cuts or by releasing them, the Saints have some major needs — especially on defense.

The Saints may have partially filled one of those needs by getting Galette to agree to a new contract. The speedy Galette will switch to linebacker as the defense transitions to a 3-4 alignment under new coordinator Rob Ryan. Galette could fill a role as a rush linebacker after recording 4.5 sacks in 2011 and a career-high five last season despite missing four games with an ankle injury.

Depending on how they view the players they have on the roster and how they plan to use them — and if Smith and/or Vilma return — the Saints also could take a long look at bringing in a nose tackle, a defensive end and another linebacker if they have cap space.

Cornerback is another area of need, either through free agency or the draft. The Saints are scheduled to have six picks in the April 25-27 draft, including the 15th selection in the first round.