Lace with little dough (10)

I believe the answer is:

shoestring

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'lace with little dough' is the definition.
'shoestring' can be an answer for 'lace' (I've seen this before). I'm unsure of the 'with little dough' bit.

'lace with little dough' is the wordplay.
'lace' becomes 'shoe lace' (shoe lace is a kind of lace).
'with little dough' becomes 'string' (I can't explain this - if you can you should believe this answer much more).
'shoe'+'string'='SHOESTRING'

Can you help me to learn more?

(Other definitions for shoestring that I've seen before include "Barely sufficient funds" , "Minimal amount of money" , "Lace" , "for securing a trainer?" , "Very little money" .)

I've seen this clue in the Sydney Morning Herald.

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