EAST RUTHERFORD, N.J. -- Jason Pierre-Paul is feeling better every day about the condition of his damaged right hand, his ability to get better and his future in football -- which he hopes is with the New York Giants.

"This is the team that drafted me, I love it here and I want to finish my career here," Pierre-Paul said after Giants practice Wednesday.

Pierre-Paul is scheduled to be a free agent at the end of this season, and his chances of returning are tied to the way he plays over the final five games of the season and what his contract demands are relative to what the Giants think he's worth. There's been a lot of mystery surrounding Pierre-Paul since the July 4 fireworks accident that cost him his right index finger, but since he's returned, the Giants have been pleased with what they've seen from him on and off the field.

Jason Pierre-Paul says he wants to be back with the Giants next year and finish his career with the team as he continues to improve on the field and feel better about his damaged right hand. AP Photo/Julio Cortez

He admits he's still working through things, and his oft-repeated line is, "Everything is new to me." But he was excited Wednesday about a new development.

For the first time since his accident, Pierre-Paul said, he was able to practice rushing from a three-point stance with his right hand on the ground instead of his left. As a right defensive end, it's to Pierre-Paul's benefit to put his right hand on the ground and turn his head and body inward to give him the best possible advantage at the snap. Rushing with his left hand on the ground was unfamiliar and likely robbed him of some of his first-step quickness.

So being able to play with his right hand on the ground, as he hopes to Sunday against the Jets, would be a big step in Pierre-Paul's recovery.

"It made a big difference," Pierre-Paul said. "And it felt good. So I'm super-excited to see what I'm going to do Sunday against the New York Jets."

Pierre-Paul is still wearing a bulky, mitten-shaped club on his right hand, and he admitted it's not easy to balance on it, but he was surprised he was able to do it as comfortably as he was Wednesday and believes it's a positive sign for things going forward. He expects to wear the club for the remainder of this season. He's been experimenting with different kinds of four-fingered gloves but hasn't found one that allows his hand to feel comfortable enough to play.

Wednesday morning, in their pre-practice injury report, the Giants said Pierre-Paul would be limited in practice because his hand was sore. After practice, Pierre-Paul said that was not the case.

"I did everything. Scout team, everything," Pierre-Paul said. "Not limited at all. I was giving everybody problems out there today."