Kansas City, Mo. ? The Kansas City Chiefs reached a deal Friday with Miami cornerback Patrick Surtain and will send the Dolphins their second-round pick.

The three-time Pro Bowler could go a long way toward shoring up one of the NFL’s worst defenses. A Chiefs spokesman said Surtain at midmorning still was in Miami, but later Friday would be in Kansas City to take his physical.

As compensation for the player, whose 25 interceptions the past three seasons lead all NFL cornerbacks, the Chiefs gave Miami their second-round pick in today’s draft — something general manager Carl Peterson had been reluctant to do. What apparently clinched the deal was Miami’s willingness to switch fifth-round picks, moving Kansas City nine spots higher.

“I’m very pleased,” Chiefs coach Dick Vermeil said. “He’s an impact player who can help a defense that needs help. He won’t need any grooming or more experience.”

The Chiefs’ poor defense, near the bottom of the league, has wasted the consistent production of a top-flight offense that sent five players to the Pro Bowl last season.

“We’ve given up too many big plays,” Vermeil said.

Acquiring Surtain completes the aggressive plan Peterson had laid out to get a linebacker, safety and cornerback before the draft. Several weeks ago, K.C. signed free-agent middle linebacker Kendrell Bell and safety Sammy Knight, as well as reserve pass-rush specialist Carlos Hall.

Surtain’s 29 career tackles are tied for third in Dolphins history. The 5-foot-11, 192-pounder will play on the right side opposite Eric Warfield, who has been the only consistent performer in a secondary that continuously was torched for three straight years.

“Any time you add a player of my caliber and Sammy’s, and Kendrell Bell and Carlos Hall, of course your defense is going to get better,” Surtain said by cell phone as he rode from the airport en route to his physical.

“At the same time, they’ve had some good defensive players in the past. You can’t discount those guys. You need the full 11 to get the job done. It’s still a team effort.”

The Surtain deal had been more than a month in the making, but getting it accomplished before the draft gives the Chiefs more options.