Now, they're eager to get after Eli Manning.
Under new coach Dan Quinn, the Falcons came into the season intent on bolstering their pass rush. They drafted defensive end Vic Beasley with their No. 1 pick, signed end Adrian Clayborn in free agency, and focused on building depth so everyone could stay fresher.
While Atlanta failed to record a sack in its season-opening win over the Philadelphia Eagles, Bradford was hit eight times and continually forced to move out of his preferred spot in the pocket. A pair of hurried throws wound up being interceptions.
''They did a very good job,'' cornerback Robert Alford said. ''It helped us out a lot in the (defensive) backfield.''
Quinn said the performance against Philadelphia was only the beginning.
''We've got a long way to go to be where we want to get to,'' the rookie coach said. ''One of things I'm pleased about is we're not near as good as we're going to be.''
While Beasley is being groomed as the go-to pass rusher, playing the so-called ''Leo'' position on the weak side in Quinn's 4-3 defense, no one on the defensive line has been credited with more than 7 1/2 sacks in a single NFL season.
Quinn, therefore, is counting on a team effort - including linebacker O'Brien Schofield, who can also play rush end when the Falcons are in a nickel secondary - to keep quarterbacks guessing.
Seven players got hits on Bradford, with Jonathan Babineaux being the only one with as many as two.
''We've got a good group of guys gelling together,'' said Babineaux, who has played for the Falcons longer than any of the linemen. ''(Quinn) wants waves of guys coming after the quarterback. That's the way it's going to be all year long.''
The 33-year-old Babineaux, a full-time starter the past seven seasons, is adjusting to a new role as a backup.
But it doesn't really seem to matter who's on the field first. Everyone is going to get plenty of playing time in Quinn's scheme.
''He wants guys to stay fresh,'' Schofield said. ''You want to have fresh guys coming in as rushers. You want to have guys who can come in and relieve the starters and still put pressure on the quarterback. We have a good two-deep, man. I don't think it's too far of a drop-off from the starters to the second team.''
The pass rush was an obvious area of concern coming into Quinn's first season. The Falcons managed just 22 sacks a year ago, working out of a gimmicky 3-4 under previous defensive coordinator Mike Nolan, who simply didn't have enough talent to muster much pressure no matter how many different alignments and schemes he threw at teams.
Cincinnati, with 20 sacks, was the lone team that had fewer than Atlanta.
After breaking down the film from Week 1, Manning said it appears the Falcons have made a significant upgrade.
''I thought they looked great,'' the Giants quarterback said. ''A lot of times, they were just bringing four guys. Sometimes, they were bringing five. But they were getting to the quarterback, getting hits. Some of the time, the Eagles were getting the completion, but Atlanta was still getting hits on the quarterback. Those add up.''
Beasley will surely draw much of New York's attention. At 6-foot-3 and 235 pounds, he's essentially a linebacker lining up at end, using his speed and quickness to get around linemen who might outweigh him by as much as 100 pounds.
His debut was promising.
''We're off to a good start,'' Beasley said. ''I think the pressure kind of helped us to get interceptions. Even though we didn't get a sack, I think we were able to cause turnovers.''
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