But Ware is not too concerned about awards. He wants more pressures, more victories, and of course, more money.
Sack totals -- Ware led the league with seven in the final two minutes of games, and was tied for third with six fourth-quarter sacks, for the record -- seem like an overrated stat.
What is important is pressure. How many times do you get to a quarterback and force him to make a bad throw?
Ware was credited with 47 quarterback pressures the last two seasons, picking up 20 in 2008. Coach Wade Phillips is now calling the defensive signals for the Cowboys, and according to Ware, he wants pressure all over the place. To make that happen, they'll need Ware more than ever.
Greg Ellis, the second-best pass rusher on the team, was released last week. It's given Anthony Spencer the starting job opposite Ware, therefore increasing the pressure on Ware. He will see double-teams and chip blocks, where the tight end helps the tackle by holding Ware at the point of attack for about three seconds.
"It's all about being more consistent," Ware said. "It's about getting pressure. I like the aggressiveness [Phillips] has brought to the game. He has to be more involved, he's the dictator."
The Cowboys are in contract talks with Ware about a long-term deal. Dallas views Ware as one of, if not the best defensive players in the game.
And the top defensive players in the game receive big money.
Albert Haynesworth of the Redskins signed a seven-year worth about $100 million, with $41 million in guarantees. Jared Allen of the Vikings inked a six-year deal worth $74.5 million, with $31 million guaranteed. Harrison signed a six-year contract extension that pays him $51.1 million, with $20 million in bonus money.
So how much is Ware worth?
Ware and the Cowboys have talked about what Haynesworth received as the standard. Harrison's deal is not what Ware is looking for, and so then the question becomes if Ware is better than Allen.
The contract talks are interesting -- if there isn't a new collective bargaining agreement by next spring, Ware will become a restricted free agent for two additional seasons. If that happens, the Cowboys could franchise him.
"That's a bad thing on their part if they do that," Ware said of getting franchised. "I don't think anything about the CBA, everybody is going on the regular schedule and thinking we'll get a deal done and keep moving."
The Cowboys need an impact player such as Ware if they expect to knock off the Giants and the Eagles, considered the two best teams in the NFC East.
Phillips' scheme allows Ware to attack the quarterback from either side of the line, while other times he will cover a running back. During an 11-on-11 drill, for example, Ware was chasing running back Felix Jones down the middle of the field on a pass play.
If the Cowboys use Ware the right way, as they did last season, there's no telling how many sacks the team will get. Dallas led the league with 59 last season, including 19 in December.
You wonder sometimes if there is a better defensive player than Ware. He joked that there's nobody better, yet hopes he sets the standard when it comes to being the top defensive player in the league.
"I hope they do," said Ware about whether or not people recognize him as an upper-echelon player. "But there are still guys out there that are better than me, and probably aren't getting recognized, that are working just as hard as me. It doesn't bother me at all. I worked for it, and at the end of the day, when you work for something, it's deserving."