En route to 7-9 finishes the past two seasons, the Saints defeated the Tampa Bay Bucs in their 2014 finale and Atlanta Falcons a year ago -- but neither team had any chance at making the post-season.
But for the second week in a row, the current Saints (7-8) will try to put a hurt on an NFC South rival when they go against the Falcons (10-5) in the final regular-season game to be played in the Georgia Dome.
Last Saturday, the Saints put a crimp in the Bucs' playoff hopes with a 31-24 win and Sunday can possibly prevent the Falcons from earning a first-round bye with a victory over their long-time rivals.
So, for the Saints, there will still be a lot on the line when they try to close out the season with a three-game winning streak and wind up with an 8-8 mark.
"From a pride standpoint, we'd like to end up at least .500," Saints defensive end Cameron Jordan said. "If that's the best we can go for at this point, we've got to finish out on a winning note."
That it could come at the expense of the Falcons has no bearing on what they're playing for, running back Mark Ingram said Monday.
"That would mean a lot to us. ... The main thing is everyone in our team and organization, coaches and players, have a lot of pride in their careers," he said. "The main thing is for us to go out and play our best football; that's more important than spoiling (the playoff positioning) of a rival."
In addition to going out the right way, the Saints could also make a small jump from the past two seasons with their eighth win of the season -- one that they hope is a springboard to better things in 2017.
"Honestly, it is not what everyone wants to see and what our goals were, but that (finishing strong) is showing we have a young team that is showing improvement right there," said free safety Jairus Byrd.
The important thing, s they have shown the last two weeks, is not just playing out the string.
"I look more closely at just the game itself, and winning is significant, always," Payton said. "The final record still represents something that's not good enough and hasn't gotten us into the postseason. And yet, it is an opportunity to win another game."
--Saints running back Mark Ingram has a chance, for the second time in three seasons, to do something no player has done for the franchise in a decade.
Ingram, a six-year veteran, has rushed for 940 yards this season and needs just 60 more in Sunday's game with the Atlanta Falcons to become the first Saints player to notch a 1,000-yard rushing season.
The last back to do it was Deuce McAllister, now a color analyst for the Saints Radio Network, who powered his way to 1,057 yards in Sean Payton's first season as the team's coach in 2006.
"A lot of different things have happened," Ingram said of the bumpy road to the magic number all backs shoot for at the beginning of the season. "My role, I wasn't always a feature guy my first couple of seasons here. A couple of times, I missed a couple games in a season.
"Health, opportunities. Everyone hopes when they come in as a rookie they can come and be a perennial 1,000-yard rusher. but that just hasn't been the case."
If he's successful in Sunday's season finale, Ingram would become only the seventh running back in the franchise's 50-year history to reach 1,000 yards.
The first six, starting with Chuck Muncie in 1979, have a total of 11 seasons with at least 1,000 yards.
The others were produced by George Rogers (1981, 1983), Rueben Mayes (1986), Dalton Hilliard (1989), Ricky Williams (2000, 2001) and McAllister (2002, 2003, 2005, 2006).
Ingram, who has picked up 4,135 yards and averaged 4.4 yards per carry for his career, moved into fourth place on the team's all-time rushing list earlier this month behind McAllister, Rogers and Hilliard.