Suggs drew rave reviews from his teammates after running for 63 yards on just six carries, including scoring runs of 8 and 15 yards in less than 21 minutes of work during the Browns 17-10 victory preseason win over the Detroit Lions.
In two preseason games, Suggs has run for 87 yards on 11 carries. Green, meanwhile, has rushed for 47 yards on nine carries.
"They are still in competition," said Davis. "They will continue to get better every week."
The Browns don't appear to be in a hurry to declare a winner between Suggs and Davis. For now, Davis is enjoying the "nice problem" of having a pair of capable feature backs, and keeping the competition alive only seems to cull the best from both players.
"It pushes both of us to get better, to be the best that we can be," said Suggs. "Will makes some great plays and then I go out there and do the same thing. It just goes back and forth."
But it was the big plays by Suggs that had the players excited in the postgame locker room.
"He is an exceptional running back," said quarterback Jeff Garcia. "We are fortunate to be blessed with some backs that have great talent. That is counting William Green, J.J. (James Jackson) and the other guys. But Lee is one of those guys who touches the ball and is so explosive. He is able to utilize the hole that he receives and is able to make things happen on his own.
"He sees the field so well. He is a slasher and is showing that he has what it takes to be an every-down back. It is exciting to watch him play."
Suggs showed his explosiveness in racing untouched around the right end on both of his touchdown runs. "Those were some great runs," said center Jeff Faine. "Not to take anything away from William Green, but Lee hit a couple of home runs to finish off two great drives."
Green had no reason to be embarrassed with his effort against the Lions, running for 24 yards on six carries. Faine thought Green did enough to stay alive in his battle with Suggs.
"William got that fourth-and-2 when it looked like he was stopped, but he just kept driving forward," Faine said. "That was huge for us because it kept a drive alive."
NOBODY'S LAUGING NOW: The miserable preseason opener in Tennessee had Gerard Warren worried that the Browns would be the NFL's laughing stock.
The big defensive tackle felt a whole lot better Saturday.
"This was a heck of a step forward," said Warren. "We eliminated some of the mistakes and we got to the ball and tackled : But we still aren't perfect. When we watch the film, we are still going to find a lot of mistakes we are going to have to erase."
The Browns first string defense did make its mistakes, but few were committed by Warren, who finished his first half with two tackles and a big pressure of Lions quarterback Joey Harrington. Warren was also a force on special teams, bulling through the middle of the line to block a 47-yard field goal by Jason Hansen.
"I was just doing my job," Warren said. "It's amazing what guys can do when they know their job and they aren't thinking too much."
INJURY REPORT : Injuries to backup safety Chris Crocker and
second-string cornerback Michael Lehan may have the Browns a bit thinner in
the defensive backfield.
Crocker suffered a concussion during the third quarter in a violent collision with Lions tight end Casey Fitzsimmons on a 19-yard seam pass near midfield.
Lehan re-injured the left foot that forced him to miss part of training camp.
Backup left tackle Joaquin Gonzalez was carted off the field in the fourth quarter with a left ankle sprain.
CLOSING IN?: Paul Zukauskas appeared to do the most with his opportunity to win the Browns vacant starting left guard job. Enoch DeMar and Chad Beasley failed to hold on to the position in their auditions during the previous two weeks.
"I thought I did pretty well," said Zukauskas, pointing to the Browns 104 yards and 6.1 per-carry average in the first half. "I think any time you rush the ball the way we did as a unit, that means you played pretty well. There are still some things I need to improve. I came off of one block too early one time, but these are things you get better at every week."