Julio Jones had an important meeting to get to. But instead of dressing up for it, he stripped down.

With his Falcons teammates still in uniform, Jones wore a sleeveless black workout shirt as he prowled the sideline late in the fourth quarter of Atlanta’s rout of the Houston Texans on Oct. 4. When the game ended, Jones snaked through the throng on the field until he spotted Texans running back Arian Foster, who jogged over to share a quick embrace — and to conduct their business.

As they had discussed before the game, Jones handed Foster his jersey, and Foster gave Jones his. Clutching their new souvenirs, they posed for a photo.

A custom associated more with fútbol than football, jersey swapping has become as much a part of the N.F.L. postgame ritual as handshakes and prayer circles. Players consider the transaction, freighted with personal meaning, the ultimate show of respect.