Teams have until Saturday to make waiver claims or trades before an 11:59 p.m. deadline to add players to their postseason-eligible list. The Braves have been trying to add a final piece or two, to little avail.

“We’ve been active for the last 10 days,” said Braves general manager Frank Wren, who put in waiver claims on multiple players, and as of Friday had gotten just one, utility man Elliot Johnson from the Royals.

To fall to the Braves, the team with the best record in the majors, a player waived by an American League team must be passed over by 28 other teams on the waiver ladder. A player from a National League team must be passed over by 13 other NL teams before getting to the Braves.

“It’s really hard, when you have the record we have, to get anything through to us,” Wren said. “We’ve made a lot of claims and been very active in discussions, but things don’t get down to us. I was talking to another GM today and he’s been in the same boat. Their record is not far from ours, so they’re in the bottom of the heap in waiver claims as well, and nothing’s getting to him either.”

Among the many players the Braves put in a claim for was Mets outfielder Marlon Byrd. He was claimed by the Pirates, who completed a trade for him and Mets catcher John Buck. The Pirates were only a couple of spots ahead of the Braves.

Wren said other players the Braves were interested in made it through waivers, but when he called the waiving team, it wasn’t interested in trading the player. Other players were claimed by teams ahead of the Braves, and then pulled back off waivers. Once a player is pulled back, he can’t be traded for the rest of the season.

“I think of all those guys that we liked that we claimed, there’s only been one of them traded, and that was Marlon Byrd,” Wren said. “The others were all pulled back. So likely, even if we had gotten them (on a claim), they wouldn’t have traded them. But they were the kind of players that would have fit with our club.”