Deliberately lose best sleeveless garment (7)

I believe the answer is:

tanktop

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

'sleeveless garment' is the definition.
'tanktop' can be an answer for 'garment' (I've seen this before). I'm unsure of the 'sleeveless' bit.

'deliberately lose best' is the wordplay.
'deliberately lose' becomes 'tank' (I can't justify this - if you can you should believe this answer much more).
'best' becomes 'top' (top can mean the very best).
'tank'+'top'='TANKTOP'

Can you help me to learn more?

(Other definitions for tanktop that I've seen before include "turret?" , "Warm garment" .)

I've seen this clue in The Times.

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