A slight incoherence in speech (4)

I believe the answer is:

slur

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'a slight' is the definition.
(I've seen this before)

I can't explain the rest of the clue.

(Other definitions for slur that I've seen before include "Slight - stain" , "Speak indistinctly, as a drunk might" , "Speak as drunk perhaps" , "making indistinct sound" , "Disparaging remark" .)

I've seen this clue in The Guardian and The Globe and Mail.

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