He's played his entire career with the club. When it comes to Browns' history, Dawson is now in position to be in the same conversation as Lou Groza or Don Cockroft.
"It's my 12th year here, but who's counting," Dawson said.
Dawson has a career accuracy of more than 83 percent, but he thinks he can do better.
"My goals are high," he said. "They are every year. I still have a goal of going the whole season without missing a kick. That might not be realistic. Certainly, when I have time to sit down and evaluate things 83 (percent) looks pretty good, but there's still room to move it up.
"Why settle for anything less? I want to improve kickoff wise with some of the guys that we have covering and I expect us to be a pretty good kicking coverage team."
Dawson knows the NFL is about what you have done lately. Eric Mangini said Dawson is one of the more consistent kickers in the league.
Is that the best compliment a coach can give you?
"I think so because in this league it's not about your best ball it's about your worst ball," he said. "If my worst ball is going through the post, that's good. "
The Browns have a goal post in Berea that's about half of the normal width and Dawson said that has helped him.
"I spent most of the offseason kicking on the high school goalposts and they look like a mile wide," Dawson said. "When you get out here and train with uprights that are half the normal size, when you get in a game, they look wider. Any visual confidence you can gain can help you."
Colt's Debut: Quarterback Colt McCoy had a rough first outing in the scrimmage with two interceptions, including one being returned for a touchdown.
"The interception at the end of the half he had wasn't really a good decision," Mangini said. "You throw a ball like that with these athletic safeties and it could come back 99 yards.
"It was up tempo but nowhere near what it will be like. He's always been the man where he has played. This is a totally different world for him and he has to get used to it. Mechanically, he was fine, but these defensive backs have the speed to make plays that he's not used to."
Eric Liked the Scrimmage: Mangini said the Browns accomplished a lot during the scrimmage and overall, he was pleased.
"I thought it was the best run scrimmage that I've been involved with in the last five years," Mangini said. "We were able to see a lot of guys in their roles in a game type setting. It allowed us to work on some things that we normally don't get to work on.
"Overall, it was a very productive day and a lot of things to coach off of. And because none of it was scripted, it's a good coaching tool."
Lessons Learned: DB Gerard Lawson was arrested with DUI/Hit Skip charges in an incident later the same night as the Browns scrimmaged at Cleveland Browns Stadium.
Mangini said he talked with Lawson, who was at practice Monday.
"Gerard is here and I told him I'm disappointed in him putting himself in this position," Mangini said.
Mangini said he tries to stress to the players that they have to be careful when they're out on the town.
"I don't want any incidents," Mangini said. "Any problem affects the whole group and we're all in it together."
The Brown team won last Saturday's scrimmage and was allowed to stay out after curfew. Lawson was on the White team, but Mangini said Brown Team captains linebacker Eric Barton and quarterback Jake Delhomme agreed to let the White team have relaxed curfews as well.
"I talked to him about it," Mangini said. "Social media is a great way to talk with the fans but the players have a responsibility for the way they use it. They are responsible for their actions. I don't expect people to stop using it, but they can't have too much information. Like anything else you have to do it in the right way."
Tweeting Eric: Mangini was asked if he would be posing updates on Twitter.
Mangini said he doesn't intend to start posting "tweets" even though at least two NFL head coaches are, including the Seahawks' Pete Carroll.
"Are you lobbying me to tweet?" Mangini asked the media." No, no. Not in the near future."
Hardesty Update: Running back Montario Hardesty will not play in the preseason opener Saturday against Green Bay according to Mangini.
"Hopefully, next week," Mangini said.
Haden Doesn't Have to Start: Mangini said that cornerback Joe Haden might not start, but that doesn't mean the overall seventh pick in the draft is a failure.
"He's done some good things, as of late and I'll be curious to see his development and he will get an opportunity in the next couple weeks to see how he will contribute," Mangini said. "They all develop differently. It's my job to make sure he can help us win and everyone has a legitimate opportunity to make their case, no matter how much they're paid or how high they were drafted."
Haden returned kickoffs in the scrimmage and Mangini said Haden was the backup kick returner at Florida.
"I don't think we have established a No. 1 backup (to Josh Cribbs)," Mangini said. "It was an opportunity to see (Haden) in that setting. We'll continue to look at it but we haven't established a backup yet."
No Go: DL Shaun Rogers, DL C.J. Mosley, DB Coye Francies, LB Titus Brown, P Dave Zastudil, RB Montario Hardesty, LB David Bowens and DB Brandon McDonald did not practice. RB Peyton Hillis and DL Brian Schaefering were back at practice.
Bad Snaps: QB Colt McCoy mishandled two snaps in team drills. However, OL Shawn Lauvao and OL Billy Yates were running laps leading to believe they were mistakes by the centers. Speaking of centers, ,OL Alex Mack also ran a couple of laps for mistakes.
Delhomme Clicks: QB Jake Delhomme hooked up with TE Ben Watson, WR Mohamed Massaquoi and WR Brian Robiskie in the two-minute drill. He also threw downfield to Hillis on a nice play earlier in practice. Delhomme also overthrew Massaquoi in the scrimmage.