Saints currently in line for a 3rd round comp pick in 2021

https://overthecap.com/compensatory-draft-picks-cancellation-chart/
As long as we don't sign any big name unrestricted free agents, we should be good. A signing like Malcolm Jenkins does not effect this exercise, as he was a cut player.

There are many teams that have mastered this art, and intentionally only sign cut players or trade for veteran talent, and we may finally see our Saints land a pick from this system. Long way to go though.