For Saints coach Sean Payton, facing kick return ace Devin Hester four times since 2006 had been enough. Now, after Hester agreed to terms on a free-agent contract with NFC South rival Atlanta, Payton’s charges might have to deal with him twice each season through 2016.

The Falcons announced Hester had agreed to terms with them on Thursday afternoon. ESPN’s Adam Schefter reported the deal was for three years.

Among other distinctions, Hester has the most career punt return touchdowns (13) in NFL history and most punt return yards (3,241) among active players after eight seasons with the Chicago Bears.

The Saints are well aware of how dynamic Hester can be. In a 2007 Saints defeat at Soldier Field, he had a 64-yard touchdown off a punt return. He also had a 55-yard touchdown reception that game.

In 2008, the Bears beat the Saints in Chicago again after Hester drew a 38-yard pass interference penalty to set up a game-winning field goal in overtime. Both of those losses eliminated the Saints from playoff contention, and they denied the Saints the chance to avenge the painful 2006 NFC Championship Game loss in Chicago.

Hester, though, was strictly returning kicks at the end of his time in Chicago, and the Saints have since beaten the Bears in New Orleans in 2011 and at Soldier Field last year. Chicago released him recently.

Nonetheless, the respect Payton had for Hester was obvious as the 2013 showdown neared.

“He’s arguably the most decorated returner in our league’s history, and that’s just a fact,” Payton said. “That’s a big deal in this game.”

Other Saints free agency tidbits

— Brian de la Puente, the Saints’ starting center since 2011, wrapped up a free-agent visit with Washington apparently without agreeing to a deal. ESPN’s Mike Triplett reported on Thursday that de la Puente was mulling his options, which included Washington, the Saints and other teams.

— Former Saints receiver Lance Moore, released earlier in March, appears to have wrapped up a free-agent visit to Pittsburgh without agreeing to a deal on the spot, per a number of reports on Thursday. However, wide receiver Jerricho Cotchery — whom Pittsburgh had targeted in free agency — agreed to a deal with Carolina on Thursday; it remains to be seen what, if anything, that could do with Moore.