With chest uncovered, slept so badly (7)

I believe the answer is:

topless

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'with chest uncovered' is the definition.
I can't tell whether this defines the answer.

'slept so badly' is the wordplay.
'badly' is an anagram indicator (letters in the wrong order).
'slept'+'so'='sleptso'
'sleptso' anagrammed gives 'TOPLESS'.

Can you help me to learn more?

(Other definitions for topless that I've seen before include "Bare-breasted" , "With chest totally exposed" , "Bare from the waist up" , "Leaving the breasts uncovered" , "Wearing no clothing above the waist" .)

I've seen this clue in The Telegraph.

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