McMahon conceded Tuesday that the Saints have done a poor job covering kicks, and although he made it clear that blame should be spread around, it was special-teams captain Troy Evans who was cut shortly after the day's practice session.
"The last two games, we have not covered kicks very well at all. It's obvious," McMahon said. "When you put the film on and you look, it'd be easy if it was one guy. But we've had our share of inconsistencies."
Payton, in a statement, said that "it's always difficult when you have to make decisions such as releasing players that have contributed as much to the Saints as Troy has. Troy was our special-teams captain the past two seasons and provided us with tremendous depth at the outside linebacker position the past three seasons."
Evans, before he learned he'd been cut, said he couldn't sleep after the Saints allowed a 52-yard kickoff return and 40-yard punt return at New England in their preseason opener.
"We know what we do wrong. We see it," the nine-year veteran said. "And that's the thing with special teams. You make one little mistake, and it can cost you, and it looks bad because it's 60 yards."
McMahon and Evans said missed tackles have been part of the problem. They said other mistakes included players being pushed out of their lanes as they advance downfield or allowing the returner to get to the outside when the assignment was to force the return toward the middle.
Payton is trying to be patient, noting that some inconsistency on special teams is common early in the preseason because so many young players are rotated onto the field as coaches try to decide whom to keep and whom to cut.
"We've got a lot of guys going in and out of the games, and so more importantly, it's who's going to play in those core units," Payton said. "A lot of the decisions we make with the final roster is predicated on how guys play in the kicking game."
"Hey, when things aren't going the way they need to go, let's get the dang thing fixed," McMahon said. "There's definitely a sense of urgency with these guys, and they understand. They look at the film and they see it and go, 'We've got to get that right.' They can see where the mistakes are. We all can. It's glaring."
The undercurrent to such problems this preseason is that the Saints were among the worst in the NFL last season in the same areas. New Orleans ranked 29th on kickoff coverage and 32nd -- dead last -- in punt coverage.
The Saints inserted more defensive starters on special teams during the playoffs, and the coverage units played a role in the run to the Super Bowl. Opponents' punt-return averages dropped from 14.3 yards in the regular season to 3.8 in the playoffs, and opponents' kickoff-return averages dropped from 24.5 yards to 23.6.
"Special teams is like its own entity. You've got guys who specialize in it, and that's what I do, and I take a lot of pride in it," backup safety Chris Reis said. "(The struggles are) one of those things you can't really figure out. You've got to let it go, keep working hard and keep pushing through, and you'll start gelling. It'll come together, we've just got have that nasty, attack attitude."
Notes: The Saints also waived WRs Mark Bradley and Rod Harper, G Tim Duckworth and CB Danny Gorrer. ... Starting CB Tracy Porter was given the day off from practice with a sore knee. ... Rookie TE Jimmy Graham (ankle), S Darren Sharper (knee), LB Clint Ingram (knee) and LB Stanley Arnoux (ankle) also sat out. ... Longtime New Orleans Times-Picayune columnist Peter Finney will present Saints QB Drew Brees with the Professional Football Writers of America's "Good Guy Award" before Friday's game. Finney, 82, is in his 64th year covering New Orleans-area sports and this year was honored at the Pro Football Hall of Fame for distinguished service. The PFWA's "Good Guy Award" goes to the NFL player who was deemed the most helpful to the media.
The Associated Press contributed to this report.