Sordid stuff: tweet, we hear, going for a song (4,5)

I believe the answer is:

dirt-cheap

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'going for a song' is the definition.
('going for a song' means sold cheaply)

'sordid stuff tweet we hear' is the wordplay.
'sordid stuff' becomes 'dirt' (dirt is a kind of stuff. I am not sure about the 'sordid' bit.).
'tweet' becomes 'cheep' (I've seen this before).
'we hear' indicates a 'sounds like' (homophone) clue.
'cheep' is a homophone of 'cheap'.
'dirt'+'cheap'='DIRT-CHEAP'

Can you help me to learn more?

(Other definitions for dirt-cheap that I've seen before include "Extremely inexpensive" , "Rock-bottom" , "Hid carpet, being unclean and inexpensive" , "Cut-price" , "Inexpensive (as muck?)" .)

I've seen this clue in The Telegraph.

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