Inverted pieces fitting nicely (4)

I believe the answer is:

snug

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'inverted pieces fitting' is the definition.
The answer and definition can be both man-made objects as well as being singular nouns.
Maybe there's a link between them I don't understand?

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for snug that I've seen before include "Close fitting but comfortable" , "Bar-parlour" , "Well protected or concealed" , "Cosy and comfortable" , "Compact" .)

I've seen this clue in The Independent.

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