Under Falcons general manager Thomas Dimitroff, the franchise has a spotty free-agency record since 2008.

The legal contact period for the next group of free agents opened Saturday and players can start signing with new teams at 4 p.m. Tuesday. The Falcons, with nearly $30 million in salary-cap space, certainly will look to fill some of their holes in free agency.

“We’re good from a cap standpoint as far as entertaining certain options in free agency,” Dimitroff said.

However, the Falcons will proceed with caution.

“That doesn’t necessarily mean we are going to go big or go home,” Dimitroff said. “It does mean, however, that we’ll be very mindful of what may be out there and what may fit into our areas of need.”

The free-agency path to improving the roster has indeed difficult for Dimitroff.

“There is no perfect world in free agency,” said ESPN analyst Bill Polian, a former general manager and six-time winner of the executive-of-the-year award. “From a club standpoint, it’s very difficult. I found it the most difficult thing I had to do as a general manager on virtually every front.”

In 2008, the Falcons hit the jackpot with the signing of running back Michael Turner to a six-year, $34.5 million contract. Turner carried the offense while quarterback Matt Ryan was developing, as he rushed for 6,081 yards and 60 touchdowns over five seasons.

Turner went to two Pro Bowls and was named All-Pro once before he was released last March.

In 2010, the Falcons lavished a six-year, $57.5 million deal on cornerback Dunta Robinson, who was leaving the Houston Texans. Two years into the deal they were renegotiating, and they released him last season, halfway through the original contract.

After the lockout in 2011, the Falcons tried to sign defensive end Charles Johnson from the Carolina Panthers. When the bidding got out of hand they backed out. Their fallback move was to sign Ray Edwards to a five-year, $27.5 million contract.

Edwards, who seemed more concerned about boxing and modeling underwear, was eccentric and a bust. He played in 25 games and had only 3.5 sacks. A total of $11 million of his deal was guaranteed.

Last season, the Falcons signed veteran running back Steven Jackson and defensive end Osi Umenyiora to modest contracts. The Falcons reportedly have asked Umenyiora to take a pay cut only one year into what was supposed to be a three-year, $12 million contract.

Jackson, who was supposed to replace Turner, battled through injuries during an unproductive first season in Atlanta.

“Fans want you to go out and play fantasy football,” Polian said. “That’s the last thing you should be doing because that money, if you miss, is gone and never comes back. I highly (detest) that approach.”

But after an historic free-fall from 13-3 to 4-12 last season, the Falcons have major retooling projects. Both the offensive line and all levels of the defense need upgrades. It’s impossible to fix them all internally and through the draft, so free agency is of particular importance this offseason.

In addition to addressing their lines, safety Jairus Byrd, a three-time Pro Bowl player, could be in play for the Falcons.

“Jairus Byrd is a guy who doesn’t run fast on the watch, but has great ball skills and instincts,” Polian said. “The central core point is system fit.”

Also, offensive linemen Jon Asamoah and Geoff Schwartz are expected to attract interest from the Falcons.

“Offensive line is the one area maybe free agency can benefit you or maybe you need to try and make it benefit you,” Polian said. “If you have a lot of spots to fill. … on the offensive line it’s virtually impossible to fill them all with rookies.”

The Falcons struggled to protect quarterback Matt Ryan last season. Dimitroff has acknowledged his missed assessment of the readiness of some players — 2012 draft picks Peter Konz and Lamar Holmes — to play last season.

So, this offseason they are trying to upgrade center, right guard and right tackle. They are set at left guard with Justin Blalock and hope that left tackle Sam Baker can return to his 2012 form after missing most of last season after undergoing knee surgery.

“You almost are forced, if you have a lot of holes to fill on the offensive line to do it through free agency,” Polian said. “So, then the choice of the players that you choose is critical. Do they fit? Are they good people? Do they have longevity? All those kinds of things. Those are the decisions that you have to make and they are not easy.”

The Falcons also want to upgrade the defensive line and boost their anemic pass rush. Defensive tackles Linval Joseph, Paul Soliai and Randy Starks are expected to attract interest from the Falcons. Defensive ends Michael Johnson, a former Georgia Tech standout, and Michael Bennett are the top-rated pass-rushers available.

“There is no mystery here,” Dimitroff said. “We know that we need to continue to build along our fronts.”

Polian would advise Dimitroff to proceed with caution.

“These (free agents) are essentially ‘B’ players, whose agents are looking for ‘A’ money,” Polian said. “There are some situations that you’re forced to deal with and you just bite the bullet and do it.”