Moore, the team's third-leading tackler with 23 stops, has yet to be flagged or fined for an illegal hit through three games after being fined almost $75,000 last year. He told ESPN he received a warning letter from the league this summer.
"My eyes have been open for a while," Moore said. "They just warned me to watch out for my hits. But I can't think about just myself. I've got to think about that it puts my team in messed up situations when I get a 15-yard penalty."
The Falcons have been flagged for unnecessary roughness twice this season, both on offensive players: receiver Roddy White and tackle Lamar Holmes. Moore's lone penalty thus far was a defensive pass interference.
"I'm becoming a smarter football player, No. 1," Moore said. "That's not in my plan to go out there and be cautious. Some of my previous penalties, they weren't dumb. They were just hitting the guy helmet-to-helmet.
"It's a long season, so I don't want to jinx myself. I just have to pick my battles. I can't afford those flags."
Falcons coach Mike Smith appreciates Moore's attempt to tone down the illegal hits. Moore was flagged for unnecessary roughness three times last season and five times in the three seasons prior to that, including three times during the 2010 campaign. He didn't play much as a rookie in 2009.
"There's a strike zone and that's something that we really emphasized this offseason, not just to William, but to everyone," Smith said. "One of the areas we wanted to improve in was our tackling. So far, I think we've done a good job of tackling, specifically William in terms of understanding what the strike zone is and what's safe for him and safe for the player he's going against.
"I think he's done a very good job through the first three games. I think a lot of it has to do with the emphasis that we put in during the offseason. Even though you can't practice in pads, we worked on different drills with tackling. And I think it has paid dividends."
Moore's fines from last season included $22,050 for hitting former Seattle Seahawks receiver Golden Tate, $21,000 for violating the crown-of-the-helmet rule against the New Orleans Saints in the season opener, $15,750 for striking Arizona Cardinals quarterback Carson Palmer with the crown, and $15,700 for striking New England receiver Kenbrell Thompkins in the head.
Moore saved a little money in the end.
"I won two appeals," Moore said. "One, I think, got wiped away completely. And the other one was reduced. I can't even remember the numbers. I just know I was happy when I looked in the mail one day."
Moore doesn't want to end up like Washington's Brandon Meriweather, who was suspended for his illegal hits. If he continues to keep his hits clean, Moore won't have to worry about waiting on a FedEx envelope.