Two arbitration cases down and one large case to go for the Braves, who have a Feb. 17 arbitration hearing with Craig Kimbrel that could go a long way toward determining whether he fits in the team’s future payroll.

The Braves signed Freddie Freeman to a franchise-record eight-year, $135 million contract and Jason Heyward to a two-year, $13.3 million deal Tuesday, thus avoiding going to hearings with two of their three young stars who were unsigned after last month’s arbitration salary-swap day.

But unless they work out a multiyear deal with Kimbrel before Feb. 17 — and that seems unlikely — the Braves face the possibility of paying the All-Star closer $9 million in 2014. That would obliterate the record first-year arbitration salary for a reliever and represent nearly a 13-fold raise over Kimbrel’s 2013 salary. And he just might get it.

A three-person arbitration panel would have to choose between the $9 million salary and the $6.55 million proposed by the Braves when the two sides exchanged salary-arbitration figures Jan. 17.

Baseball’s most dominant reliever the past three seasons, Kimbrel became the youngest closer (25) to collect 50 saves when he tied for the major league lead with 50 in 2013. The Alabama native had a 1.21 ERA with 98 strikeouts in 67 innings, and he’s led or tied for the NL lead in saves in each of his three seasons as a full-time closer.

Kimbrel has unprecedented statistics to begin his career, including a 1.39 ERA with 381 strikeouts in 227 1/3 innings.

His salary would be determined by a panel of three independent labor arbitrators. They’ll listen to both sides during the half-day hearing in a St. Petersburg, Fla., hotel conference room.

If Kimbrel is awarded the $9 million salary for 2014, he could expect to get at least $14 million a year from now if he hasn’t signed a long-term extension and goes through the arbitration process again. At that price, he could strain the payroll.

Heyward’s $13.3 million deal includes performance-based escalators that can increase his salary in the second season. He’ll have base salaries of $4.5 million in 2014 and $7.8 million in 2015, plus a $1 million signing bonus.

“I’m just excited that I don’t have to worry about the (arbitration) process any longer,” said Heyward, who will be eligible for free agency after the contract expires. “The business part, it can be a distraction. I’m glad it’s not.”

The $300,000 difference between the one-year salaries proposed by Heyward ($5.5 million) and the Braves ($5.2 million) on Jan. 17 was the second-smallest among the 38 players who swapped figures with teams.

Heyward missed two months of the 2013 season recovering from two surgeries — one an appendectomy and one for a broken jaw after he was hit by a fastball. He played in 104 games and made $3.65 million while hitting .254 with 14 homers in 440 at-bats. That included .322 with a .403 on-base percentage and six homers in 118 at-bats from the leadoff spot.

“Last year was such a tough year physically, through no fault of his own,” general manager Frank Wren said. “So it also made it difficult for both sides in an arbitration situation because it’s hard to pin a number when you’re comparing to players who played a lot more or played less.

“And Jason’s an important part of our team, so this probably was the best way to answer some of those questions on both sides, was to get a two-year deal.”