Crossword Genius

Leave little room for airport customs inspection? That's easily decided (4-3-4,4)

Ross

I believe the answer is:

open-and-shut case

I'm a little stuck... Click here to teach me more about this clue!

'leave little room for airport customs inspection?' is the definition.
I don't know anything about this answer so I cannot judge whether this works.

'easily decided' is the wordplay.
I cannot quite understand how this works, but
'easily decided' could be 'openandshut' (I've seen this in another clue) and 'openandshut' is located in the answer.
The remaining letters 'case' is a valid word which might be clued in a way I don't see.
This explanation may well be incorrect...

'that's' is the link.

Can you help me to learn more?

I've seen this clue in The Times.
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