The Giants are waiting to see “the old JPP” from Jason Pierre-Paul this season, but the defensive end with the mangled hand, the one-year contract and the need to prove to the world that he can still succeed in the NFL, is shooting for something beyond that.

“I’ll be better than the player I was,” Pierre-Paul boasted on Tuesday after the team’s first practice of their voluntary minicamp.

Why the optimism? Pierre-Paul said he’s in the best shape of his life and has reported to the offseason program lighter than ever (he wouldn’t say how much lighter, only that he normally comes in around 285). Just the fact that he’s with the team at this point in the process is a change from previous offseasons.

“It would have been better last year if I was here,” he said of skipping the voluntary parts of the schedule while waiting to sign his franchise tag tender. He has a new supporting cast, looking down the line on Tuesday and seeing Damon Harrison and Olivier Vernon alongside him. He said he will not require any further surgeries on his hand. “It’s a straight shot for me,” he said. And he is eagerly anticipating the arrival of a new glove that will further improve his ability to grip. “It’s on the way,” he said. “Stay tuned.”

All of which can simply be filed under late April optimism. The real test will be when he gets on the field and has to actually perform.

“We’ll have to get out there and we’ll have to do some offense vs. defense where he has a chance to work and do those types of things,” Ben McAdoo said, “but he’s already ahead of the game compared to last year.”

advertisement | advertise on newsday

Pierre-Paul opened up about last summer’s fireworks accident to Sports Illustrated in an article published earlier this month. He said he did so to show that he was “past” those issues.

“I’m looking towards my future now, which is bright,” he said.