You haven't seen the best of the New Orleans Saints.

Of course, Coach Sean Payton likely wouldn't want it any other way after five games have been played. Entering Sunday's game against Jacksonville (2-3) at TIAA Bank Field in Jacksonville, Fla., the Saints are 4-1 and lead the NFC South Division.

The team steadily has shown improvement; it's 3-0 since starting quarterback Drew Brees was sidelined by a torn thumb ligament that required surgery, with the team riding a different mode of transportation to victory in each game. And for each mode, there's room to grow.

"I think we've shown signs situationally," Payton said. "I felt last week (in a 31-24 win against Tampa Bay), we played better in the red area offensively (3-for-4, after going 0-for-4 the week before) and defensively, we were better on third down (Tampa Bay was 3 of 11).

"In all three areas, when we've needed a play, we've gotten it. I felt special team-wise, especially right through the middle stretch of that five weeks, we had some game-changing plays. Defensively, our ability to pressure the quarterback – not necessarily sack the quarterback – but our pressures, I've been encouraged there.

"And yet, there's so much when you watch the tape – and look, I'm not trying to sound displeased – we're sitting here with the record we have and yet, I don't feel like we're playing near our best football. And we've got to work to get that corrected."

One of the most significant jumps for New Orleans has been the run defense. That's not totally surprising, given that the Saints allowed just 80.2 rushing yards per game last season, second-fewest in the league.

But since a rocky start to 2019 – 180 rushing yards allowed and 7.8 yards per carry against Houston in the season opener – the Saints have dropped the numbers to 91 yards per game and 3.7 yards per carry in the last four.

"I think we're deeper in the defensive line than we were a year ago, and I think we're better across the board," Payton said. "I think we've got good additions, I think (defensive line coach) Ryan (Nielsen) and B.Y. (pass rush specialist coach Brian Young) have done a great job. The depth has helped us – we dressed eight defensive linemen last week, which is a high number. And then at linebacker, we've had some additions. But I think overall our front is playing better.

"I just think that we've brought in good pieces to already help players that were there. It's hard to find good defensive linemen; you have to draft them or pay a lot for them. And we've been able to do that."