Bryant turned down both, and said Dallas will have to show similar restraint at game time since the Giants are hot and his team is not going into an NFC East showdown with playoff implications.
''You can't be going out there trying to look for home runs,'' Bryant said. ''You've got to let that stuff come. That's what we're going to do.''
The freshest memory for the Cowboys is a 49-17 loss to New Orleans before last week's bye. They weren't competitive, then watched over the weekend while Philadelphia (6-5) beat Washington to move a half-game ahead of Dallas (5-5), knocking the Cowboys out of the division lead for the first time this season.
The Giants (4-6) pulled within a game of the Cowboys by beating Green Bay for their fourth straight win after an 0-6 start.
Pierre-Paul boldly predicted his 24-yard interception return - rare for a pass rusher - in the huddle before the play. He spoke of beating the Cowboys afterward, saying the Giants were ''going to put it on them,'' among other things.
''He's supposed to feel that way,'' Bryant said. ''You're an opponent. We're an opponent for them. It's great confidence.''
The Cowboys opened the season with a 36-31 win over the Giants in a game that was close despite six New York turnovers because Eli Manning threw for 450 yards.
Since then, three more quarterbacks have thrown for at least 400 yards to set an NFL record against one team.
Drew Brees would have been the fifth if the Saints hadn't been so far ahead of the Cowboys. Against New York, Dallas figures to be without its best defensive player, linebacker Sean Lee, because of a strained hamstring. And Pierre-Paul's counterpart, DeMarcus Ware, aggravated a thigh injury against the Saints.
It all sounds a little gloomy unless you're defensive tackle Jason Hatcher, who made a trip to Los Angeles during the bye and came back feeling good enough to practice Monday after missing the New Orleans game with a neck injury he's been dealing with most of the season.
''I'm so positive because we're in control of our destiny,'' Hatcher said. ''This whole six games is on us and what we do. If we don't approach it the right way, it's on us. If we go out there and handle our business, we'll be in a great situation.''
The Cowboys probably need Lee and Ware to end a three-year playoff drought, but they are getting healthier. Besides Hatcher, which was probably the best news for Dallas, rookie safety J.J. Wilcox returned to practice, making it less likely the Cowboys will have to rely on an undrafted rookie in the secondary.
Receiver Miles Austin returned to practice last week after missing three games with another hamstring injury, which might mean fewer double teams for Bryant the first game after he was targeted just twice and had one catch against the Saints.
''You put a smile on my face saying that,'' said Bryant, who is tied for third in the NFC with eight touchdowns receiving. ''It's going to be great. You've got Terrance Williams, you've got Jason Witten, you've got Miles Austin, you've got me, you've got Cole Beasley. What more can you ask for?''
A little momentum wouldn't hurt, but the Cowboys will have to wait until Sunday for that.
''Certainly, when you're feeling good about yourself that's a positive thing,'' coach Jason Garrett said. ''But the best teams, the best players are the ones that take each situation independently of the other one and do it to the best of their ability.''
Notes: The Cowboys added LB Taylor Reed to their practice squad and released DE Hall Davis. Reed was with the Cowboys in training camp and was cut at the end of the preseason.
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