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Hello,
I would like to know the exact meaning of this "swamp up" here:

'Danny (the producer on the record) didn't have to SWAMP the song UP too much, it was already swamped up pretty good when it came to him'

Thanks in advance, Jo.
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Hi,

'Danny (the producer on the record) didn't have to SWAMP the song UP too much, it was already swamped up pretty good when it came to him'

Here's what I think.

This is a reference to American Cajun music, which is sometimes said to have a "swampy" sound because the Cajun area of New Orleans has a lot of swamps. The sentence means that the music already sounded very Cajun, so the producer did not have to add much more of the Cajun sound to it.

A phrase like 'to swamp up' is uncommon, non-standard and slang-y English.

Best wishes, Clive

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Not sure, but this is the context, for others:
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Chronicles: Volume One, By Bob Dylan

Ambiguity and mystery, so potent here, have long been key to Dylan's mojo.
"Chronicles" stresses Dylan's life in New York in the early '60s and
highlights "New Morning," a 1970 album, and "Oh Mercy," a 1989 disk
that Daniel Lanois produced.

It touches winningly, if fleetingly, on Dylan's early years in
Minnesota's Iron Range and artfully weaves the artistic and the historical.
Explaining "Everything Is Broken," an "Oh Mercy" tune, Dylan writes, "Danny
didn't have to swamp it up too much, it was already swamped up pretty good when
it came to him.

Critics usually didn't like a song like this coming out of me
because it didn't seem to be autobiographical. Maybe not, but the stuff I
write does come from an autobiographical place."
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Comments  

Swamp up is an Americanism meaning to clear out or clean up.

Students: We have free audio pronunciation exercises.

Means "clean up"

The reason it means "clean up" or "clear out" is because it is something that a "swamper" does. See definition 2.a. in the American Heritage Dictionary link here:

https://www.ahdictionary.com/word/search.html?q=swamper