Mondragon was an autodidact on bass, and began working professionally in Los Angeles. He served in the Army during World War II, and then joined Woody Herman's First Herd in 1946. Over the next two decades, he became one of the more popular studio bassists for jazz recording on the West Coast, appearing on albums by June Christy, Shorty Rogers, Shelly Manne, Buddy Rich, Buddy DeFranco, Marty Paich, Claude Williamson, Georgie Auld, Chet Baker, Bob Cooper, Harry Sweets Edison, Gerry Mulligan, Art Pepper, Bud Shank and Ella Fitzgerald. Mondragon can also be heard on soundtracks for films such as The Wild One and Pete Kelly's Blues.
Mondragon never recorded as a leader.
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With Chet Baker
- Grey December (Pacific Jazz, 1953 )
- Pretty/Groovy (World Pacific, 1953 )
- The Trumpet Artistry of Chet Baker (Pacific Jazz, 1953)
- Chet Baker & Strings (Columbia, 1954)
With Georgie Auld
- In the Land of Hi-Fi with Georgie Auld and His Orchestra (EmArcy, 1955)
With Lalo Schifrin
- Gone with the Wave (Colpix, 1964)