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ENGLEWOOD (CBSMiami/AP) — Last year the Miami Dolphins were one of several teams interviewing the hot coaching prospects around the league to fill a head coaching vacancy.

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Now Miami is on the opposite end of that process.

The Denver Broncos met Tuesday with Dolphins defensive coordinator Vance Joseph, the third candidate to interview for their head coaching vacancy following Gary Kubiak’s resignation for health reasons.

“He has great leadership qualities and a strong vision of what it takes to win,” general manager John Elway tweeted after the interview that lasted several hours.

Joseph, 44, a former University of Colorado quarterback, just completed his first season as a defensive coordinator on Adam Gase’s staff in Miami, where the Dolphins ended an eight-year playoff drought.

Before that, he built a reputation as one of the NFL’s best secondary coaches while rising through the ranks in San Francisco, Houston and Cincinnati.

On Friday, Elway visited with Chiefs assistant Dave Taub , 54, who directed the league’s top special teams unit in 2016. On Saturday, he met with Falcons offensive coordinator Kyle Shanahan , 37, the architect of the NFL’s highest-scoring offense.

The Broncos cannot contact Taub or Shanahan again until their teams have either been eliminated or win their conference championships.

Joseph flew into Denver on Tuesday, 48 hours after the Dolphins’ 30-12 loss at Pittsburgh in the AFC wild-card round. The Dolphins, who ranked 29th in the league defensively, allowed touchdowns on their first three defensive series.

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This marks Joseph’s second shot at the Denver job.

He also interviewed two years ago when Kubiak was hired. The Broncos were so impressed with Joseph at that time that they wanted to make him their defensive coordinator, but the Bengals blocked the move. So, he spent another season in Cincinnati coaching the DBs before Gase hired him in Miami.

Kubiak, 55, was halfway through his four-year contract when he stepped down last week, capping a tumultuous season in which Denver (9-7) missed the playoffs a year after winning Super Bowl 50.

Kubiak’s replacement will inherit a dominant defense featuring first-team All-Pros Von Miller, Aqib Talib and Chris Harris Jr. but also an offense that needs major repairs after flopping in 2016.

Denver’s defense ranked fourth in the NFL, its offense 27th. That divide led to fissures in the locker room with members of the team’s stellar secondary jawing with the offensive linemen for failing to protect young QBs Trevor Siemian and Paxton Lynch.

Despite that disparity, Elway said maintaining his elite defense was just as important as patching his O-line again this offseason.

Although both men eventually asked out, Elway is 2-for-2 in his coaching hires. John Fox went 49-22 with four AFC West titles in four seasons and Kubiak went 24-11 and led Denver to its third Lombardi Trophy.

Miller said he trusts Elway will make the right choice again whether the coach has offensive or defensive roots.

“He’s the king of the comeback,” Miller said, “both on and off the field.”

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(TM and © Copyright 2017 CBS Radio Inc. and its relevant subsidiaries. CBS RADIO and EYE Logo TM and Copyright 2017 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)