Giants defensive end Jason Pierre-Paul (90) pressures Pittsburgh Steelers quarterback...

Giants defensive end Jason Pierre-Paul (90) pressures Pittsburgh Steelers quarterback Bruce Gradkowski (5) on a throw in the first quarter of a preseason game, Saturday, Aug. 9, 2014, in East Rutherford, N.J. Credit: AP

With every snap Jason Pierre-Paul takes this preseason, every play he makes in training camp and every smile he flashes on the field, there is a phrase that runs through the minds of all associated with the Giants. After almost two full years of limited production because of injury, the hope is that 2014 will allow "the old JPP" to return.

That's the player who dominated offenses in 2011, racked up 161/2 sacks, seemed omnipresent against the run and was on the verge of becoming an NFL Defensive Player of the Year candidate.

Even defensive coordinator Perry Fewell said last week that his defensive end looks like "the old JPP" in practices. Everyone seems to want that. Everyone except JPP. He wants to be the "new JPP." New and improved.

"I'm trying to be better than that 2011-2012 year," he said Monday, fresh off his most fluid performance since Super Bowl XLVI.

Pierre-Paul made four tackles against the Steelers on Saturday, ran around the field with ease and even got some quarterback flesh in his teeth with a hit on backup Bruce Gradkowski.

But how much better can he be in 2014 than he was in 2011?

"A lot," he said. "Every day is a learning process . . . You never can stop learning."

There's not much better than 161/2 sacks. Other than Michael Strahan's team and NFL record of 221/2.

"Yeah," Pierre-Paul said. "Maybe."

Pierre-Paul later noted that he doesn't have a number of sacks in mind for 2014, other than "unlimited." That's a word that used to be associated with his potential. After back problems (and a new wave of double-teams) slowed him in 2012 and surgery really sapped his game in 2013, Pierre-Paul is back to looking limitless.

"I thought that he really chased the ball and showed the outstanding speed that he has," Tom Coughlin said Sunday. "You saw it on the reverse, you saw him down the line of scrimmage. I thought for the plays he had in the game that he gave good effort and was in good position. The way in which he chased the ball and coming in from behind was very good."

Pierre-Paul said he was happy to report that he was not winded after trying to run down speedy rookie Dri Archer on a long screen pass early in Saturday's game against the Steelers.

"I wasn't going to catch him, but I feel good, though," he said. "That was a long run for me, so I wasn't tired at all."

It wasn't all perfect. He said he had a "false step" when closing in on Gradkowski for the hit in which he leveled the quarterback but arrived a split-second too late. The play wound up going for a 17-yard completion.

"I could have been there quicker," he said. "Those are the type of details I'm talking about [improving]. It's only in game situations can you do that. That was a game situation and I hit him, it was a great hit. I need to get there faster."

His tackle on an end-around by Markus Wheaton also required speed. Coughlin liked it. Pierre-Paul was not impressed.

"That's just turning and running to the ball," he said. "That's what I'm supposed to do. It's nothing special."

When he hasn't been able to do it for a while, though, it becomes special to see it again.

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