Davis began training camp as the Rams' No. 4 quarterback. However, he has jumped to No. 2 on the depth chart with a strong showing in preseason.
Davis has completed 27 of 44 passes for 372 yards and three touchdowns against one interception. His quarterback rating is 101.7.
''I'm not really pleased and settled,'' Davis said Tuesday after the Rams practiced under a sweltering sun at Rams Park. ''There's a lot I've got to get better at. Every day is a new day.
''It's all part of the deal. You hope you make the team and you hope you move up the ladder. You can't control anything but your attitude and work ethic.''
In the Rams' 33-14 win over the Browns, Bradford went down with a season-ending knee injury on the first drive. Cleveland defensive end Armonty Bryant beat Rams left tackle Jake Long. Bryant hit Bradford just after he had released a pass and the result was a torn anterior cruciate ligament in his left knee.
Although Hill came in for Bradford, he quickly left the game after one series that ended with a field goal.
Davis saw the most action of all the quarterbacks. He completed 14 of 22 passes for 198 yards, two touchdowns, had one sack and one interception for a passer rating of 104.0.
''We did some good things and the biggest thing is offensively, we moved the football,'' Davis said. ''I made some mistakes. There's a lot I can clean up.''
Rams coach Jeff Fisher liked what he saw from Davis against the Browns.
''He played well in the game against a lot of their starters and so he made plays,'' Fisher said. ''He's got a good feel for what we're doing.''
In preseason opener against New Orleans, Davis 10 of 16 for 134 yards and a touchdown. His passer rating was 109.9. In the second game against Green Bay, Davis competed 3 of 6 passes for 50 yards. He was sacked four times.
He followed that lackluster performance with a strong showing against Cleveland.
Now he is backing up Hill, who is in his 13th season. Davis is looking forward to working with the veteran.
''I've just been with him for a short time, but he's a great professional,'' Davis said. ''He knows how to get things done. He's a heck of a quarterback, so it will be fun to help him each week and keep this thing rolling.''
Davis went undrafted in 2012. He signed a free agent deal with the Rams and made the team. He did not play during the season.
Last year, Davis was cut but the Miami Dolphins signed him to their practice squad on Sept. 10. Davis re-signed with the Rams on Oct. 22 after Bradford tore his ACL against Carolina. Again, he did not play.
Fisher believes Davis is up to the challenge of being the No. 2 quarterback. He said Davis will play in Thursday's preseason finale at Miami.
The offense won't change with Davis playing.
''Austin's mobile. First off, he's smart. He understands what we're doing,'' Fisher said. ''He gets it. He's had a good camp so far, so obviously Austin would step up to the two spot right now if it were the start of the regular season.''
But that could change. Trade rumors are abundant in St. Louis since Bradford got hurt.
Hasselbeck is no stranger to trade talk.
''It happened early on in Green Bay when it was obvious I was never going to see any playing time (behind Brett Favre),'' Hasselbeck said. ''You know all of the quarterbacks, we like Shaun Hill. We think he's a good guy. But whenever someone goes down, you hear names mentioned.
''It's kind of like coaching searches. Every time someone gets fired, you hear about Bill Cowher and Tony Dungy and guys like that. It's the same with quarterbacks.''
NOTES: The team waived DE Sammy Brown and S Matt Daniels and placed Bradford and C Demetrius Rhaney on reserve-injured to get to the 75-player limit. Michael Sam is still in the mix for a roster spot on the defensive line.
AP Sports Writer Michael Marot in Indianapolis contributed to this report.
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