The Kansas City Chiefs' search for normalcy may go on for much longer than the remaining NFL schedule.

For Brady Quinn and Peyton Hillis, a different type of closure is at hand.

With emotions still prevalent after last week's tragic events, Quinn will try to lead the Chiefs to another victory when he and Hillis return to Cleveland to face the Browns for the first time Sunday.

Kansas City (2-10) is still grieving the death of linebacker Jovan Belcher, who killed his girlfriend and then turned the gun on himself in front of coach Romeo Crennel and general manager Scott Pioli last weekend.

Despite the tragedy, the Chiefs were on the field the following day, and beat Carolina 27-21 to end an eight-game slide amid strong emotions at Arrowhead Stadium.

"We have to deal with the events of the last few days, and it's not over, and it may not be over for some of us for most of our lives, but time heals all wounds, and so we're going to start working on the time thing," Crennel said.

A visit to Cleveland (4-8) may provide a chance for some focus for at least Quinn and Hillis.

Quinn was drafted 22nd overall out of Notre Dame by Crennel and the Browns in 2007, but never lived up to lofty expectations and was dealt to Denver for Hillis and two draft picks in March 2010. He won only three of 12 games as a starter with Cleveland, finishing his 14-game tenure there with 10 touchdowns, nine interceptions and a 66.8 passer rating.

After spending two years on the bench with the Broncos, Quinn reunited with Crennel in Kansas City and has been given a second chance following ineffectiveness and a concussion to starter Matt Cassel.

He's finally making it count. Quinn completed 19 of 23 passes for 201 yards and two touchdowns last week - his first scoring passes since Dec. 6, 2009. He was widely praised even more for his leadership qualities in a somber post-game press conference, discussing the recent murder-suicide.

"I feel like I can do a decent job of adjusting to pretty much anything," Quinn said. "I think anytime you have an opportunity to play more and get more experience, you're going to continue to grow and improve as a player."

Hillis, meanwhile, is still waiting his turn after signing a one-year contract with the Chiefs following two vastly differing seasons with the Browns.

The bruising running back was the toast of Cleveland in 2010, setting career highs in rushing yards (1,177), carries (270), receptions (61), receiving yards (477) and touchdowns (13).

He tried to turn that brief stardom into a big contract, but instead proved to be a headache in an injury-plagued 2011. Hillis was limited to 587 yards and three TDs in 10 games, and Cleveland's Joe Thomas wasn't shy about expressing his disdain for his former teammate.

"He was everything people knew about him - hard-working, blue-collar, tough, would do anything for anybody on the team," Thomas said. "All he cared about was winning, and then all of a sudden the next year, all he cared about was trying to get his new contract.

"He crippled our offense. To have Peyton going through a contract dispute and basically refusing to play, it was a big distraction. I think it was better for both sides (he left). At that point, the situation with him here was toxic and he didn't want to be here and players didn't want him here. It was better for a fresh start."

Not better for Hillis, who has 193 yards and a touchdown on 59 carries. He fired back at Thomas on Thursday.

"Joe Thomas, he can have his opinions all he wants. It's kind of like a crazy ex-girlfriend, you know? It's been over a year. Get on with it."

It's unlikely the Browns will see a heavy dose of Hillis since Jamaal Charles is among the league's top rushers with 1,055 yards with 4.8 per carry.

Cleveland, though, has held opponents to 65.7 rushing yards over the last three games, winning 20-17 at Oakland last Sunday for its second straight victory. That may have eased the pressure on embattled coach Pat Shurmur.

"I don't want to talk about my future, OK?" he said. "I'm trying to get our team ready to play the Chiefs and then after that and so on and so forth. I don't look at it that way. I'm not taking any half-swings here. We'll just play it out and see what happens.

"I feel good about where we're going, we've just got to keep going."

Part of that encouragement may stem from a season-high 475 yards of offense last week, and improvement from Brandon Weeden.

The rookie has completed 63.9 percent of his passes for 732 yards with four touchdowns and three picks over the past three games, and is coming off a season-high 364 yards through the air against the Raiders.