I'm also pretty sure I heard The Byrds' version of "Mr. Tambourine Man" before Dylan's. It hit #1 in 1965 (the same year Dylan released the song on Bringing It All Back Home). Only later did I connect the song to Bob Dylan.
The Byrds' cover of "Mr. Tambourine Man" upped the jangle ante and has been cited as a significant influence of the folk-rock explosion the late 1960s and early 1970s.
With its dozens of covers and staying power, "Mr. Bojangles" made Dylan's music accessible to a wider audience, even spawning (and I think that's the appropriate word) a rendition by William Shatner.
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