Pierce-Paul notched 16.5 sacks and made the Pro Bowl in 2011. But the 25-year-old, who was hampered last season by back and shoulder injuries, has recorded just two sacks in his past 23 games.
Asked if his goal is to get back to the "JPP" of old, Pierre-Paul responded: "I'm trying to be better than [the 2011 version]. Each year is a year for you to get better, so that's what I'm trying to do."
Pierre-Paul feels he can get "a lot better" as a player. When told that a lot better could essentially represent a record-breaking campaign, he responded with a laugh: "Yeah. Maybe. Or get another Super Bowl."
He doesn't have any specific numbers in mind as far as his statistics are concerned.
"Nope. Unlimited," he said.
Last season, Pierre-Paul acknowledged that he wasn't having as much fun playing football because he was hurt.
"I felt the pain. That was basically it," Pierre-Paul said. "No one wants to be injured or whatever, but it comes with the game. You never know if you're going to get injured, and you just have to fight through it."
Pierre-Paul just wants to make it through training camp healthy. He looked like his old self in his team's second preseason game on Saturday night against the Steelers, recording four tackles.
Last season, the Giants finished tied for 25th in the NFL with 34 sacks. Since then, they let veteran Justin Tuck, who had 11 of those sacks, depart for Oakland in free agency. So the pressure is certainly on Pierre-Paul to become the dominant pass-rusher he used to be.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.