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.

Added Kelce, who spoke right 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.”