St. Joseph, Mo. ? The Kansas City Chiefs have demonstrated a willingness under general manager John Dorsey and coach Andy Reid to give players who have run into trouble a second chance.

They’ve also proven there’s no such thing as a third.

Take the case of Justin Cox, a defensive back from Mississippi State. He went undrafted after missing the final three games and the Orange Bowl last season following a domestic violence arrest — a charge that was ultimately dropped — and the Chiefs gave him a shot. But when Cox was arrested again this summer, it took them less than 24 hours to send him packing.

“I wouldn’t say there’s a hard and fast policy because every situation is different,” Chiefs chairman Clark Hunt said. “It’s up to John and his staff to do the research when a player has an incident and make a judgment call whether it’s going to work out. That particular situation, it didn’t, but John is very aware we don’t want guys who are going to be a problem.”

The Chiefs do want players who can help them win, though, and therein lies the balancing act that all NFL teams face: When do you take a risk? When do take a pass?

In the three years since Dorsey and Reid have been in charge, the Chiefs have added numerous players with checkered pasts, and so far they’ve mostly steered clear of trouble.

Tight end Travis Kelce was their third-round pick a couple years ago, even though he had been suspended in college for violating team rules. Not only has Kelce developed into one of the most dynamic tight ends in the game, he has also matured into a locker room leader.

“A little bit more accountability,” Kelce replied, when asked how he’s changed.

The Chiefs also took a chance on cornerback Phillip Gaines in last year’s draft. He had run into trouble at Rice, but his size and speed made him an intriguing prospect. Fast-forward to this year’s training camp and Gaines is competing for one of the starting jobs.

But perhaps never have the Chiefs taken on so many players with spotty pasts as this past season, beginning with the draft and continuing right on through free agency.

Their first-round pick, Marcus Peters, was thrown off his team at Washington because he could not get along with new coach Chris Peterson. But the Chiefs insist that they researched the standout cornerback, who might’ve been a top-10 pick had he stayed out of trouble, and came away confident that Peters had learned from his mistakes and was unlikely to repeat them.

“It was an emotional situation and he didn’t handle it the right way. I think he’s learned from it, just from our experience with him,” Reid said. “He was up front with us. He said, ‘I goofed,’ and that’s half the battle.”

Defensive lineman David Irving has also acknowledged his mistakes, a big reason Kansas City was willing to give him a shot as an undrafted free agent.

The former Iowa State standout was suspended after he was charged with domestic abuse against the mother of his child, a charge that was later dropped. Then, during a riot near campus during a student-run festival, Irving was photographed holding a stop sign that he argued was handed to him by another person. He was charged with theft, disorderly conduct and criminal mischief.

When he did make it onto the field, Irving was one of the best defensive linemen in the Big 12, and he could help the Chiefs absorb the loss of nose tackle Dontari Poe to injury.

“We knew he was a good football player,” Reid said. “He had some issues, obviously. John Dorsey and his crew, I thought, did a nice job getting in there and making sure with him that he would fit in here and that he kind of had things going in the right direction.”

Dorsey and Reid also thought that Cox was headed in the right direction, only to be proven wrong. But that is the tightrope they are willing to walk — star potential on one side of a very thing line, and more trouble looming just on the other.

“John and I talk about it, and he knows that we want to be a leader in the NFL,” Hunt said, “not a team that has a lot of guys that are getting in trouble.”

Notes: Chiefs defensive coordinator Bob Sutton said Tuesday that LB Derrick Johnson “is back to where he was” before his season-ending Achilles injury. … Gaines left practice early with an injury. It did not appear to be serious. … WR L’Damian Washington, who signed with the Chiefs on Monday, participated in his first practice.