Kansas City, Mo. ? The Kansas City Chiefs weren’t deterred by off-the-field issues that cost tight end Travis Kelce an entire season at Cincinnati, or injury woes and fumbling problems that plagued running back Knile Davis at Arkansas.

The Chiefs picked Kelce with the first choice in the third round Friday night and then grabbed Davis with a compensatory choice as the second night of the draft wound to an end.

“We kind of let the board speak to us today,” Chiefs general manager John Dorsey said, “and it kind of unfolded, and that’s where we are.”

The Chiefs didn’t have a second-round selection after trading it to San Francisco to acquire quarterback Alex Smith. So after picking offensive tackle Eric Fisher at No. 1 on Thursday night, they had to wait until the 63rd overall pick to snag their new tight end.

The 6-foot-5, 255-pound Kelce should provide a big target for Smith after snagging 40 passes for 599 yards and seven touchdowns for the Bearcats last season.

“I think the Chiefs are going to get someone that’s very versatile,” Kelce said shortly after his name was called. “If I had to possibly mention one guy, Jeremy Shockey, the way he plays with passion and effort that would be an awesome comparison.”

Shockey is no stranger to character questions, and Kelce brings his own to the NFL.

He missed the entire 2010 season after a violation of team rules, and Kelce disclosed Friday night that the issue stemmed from a positive test for marijuana his sophomore year.

“It was something that happened, it’s in the past and it is what it is,” Kelce said. “I’m very remorseful, and very prideful of who I am now, and the Chiefs organization is going to get who I am today, and I’m not going down that road today.”

The Chiefs had already upgraded at tight end by signing free agent Anthony Fasano to a four-year, $16 million this offseason. But with the future of Tony Moeaki uncertain because of injury trouble, Dorsey and new coach Andy Reid viewed Kelce as a good value.

He’s a strong run blocker and has enough pass-catching ability to draw comparisons to the Patriots’ Rob Gronkowski and the Lions’ Brandon Pettigrew.

Reid also has said that he intends to use two tight-end sets in Kansas City, much like New England has done with Gronkowski and Aaron Hernandez the past few seasons.

“He’s a great guy, great coach and he’s going to hold you accountable,” Kelce said. “and I love that about coaches. And I’m more than happy and more than fortunate to get a guy like Coach Reid to coach me up and get me going in the right direction.”

Davis had a monster sophomore season for Arkansas, running for 1,322 yards and 13 touchdowns. But the 227-pound running back broke an ankle as a junior, and a combination of uncertainty on the coaching staff and his fumbling problems resulted in a rough junior season.

He only ran for 377 yards and two touchdowns last year.

“I was hoping I’d get called today, but I had no idea it’d be Kansas City,” Davis said. “I’m just grateful, man. I’m blessed and honored to be a Chief.”

Reid said that LeSean McCoy had a similar fumbling problem when he was with the Eagles, and he managed to overcome it. Reid also said that the Chiefs’ front office looked into Davis’ injury history, which included a hamstring issue last season, and came away satisfied.

“He gives you a threat very similar to (Jamaal) Charles in that whenever he touches the ball, he can go the distance,” Reid said. “This is a good kid on top of all that.”

One of the dominant story lines for the Chiefs this draft remained status quo when Dorsey and Dolphins general manager Jeff Ireland failed to agree on a trade for left tackle Branden Albert.

Dorsey said that the two agreed to resume negotiations on Saturday, when the draft picks up with the fourth round. Albert has already signed a franchise tender worth about $9.3 million next season, but has expressed his frustration with a lack of long-term contract.

“All along, it’s been an ongoing process. It will be an ongoing process until the end of the draft takes place. We’ll see what happens,” Dorsey said. “All along, we’ve considered Branden a really good football player. We used the franchise tag on him. That doesn’t mean we can’t begin conversations with his representatives down the road. He’s a winning football player.”