Busy gent, healthier to move round with nothing on (2,3,10)

I believe the answer is:

in the altogether

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'move round with nothing on' is the definition.
I can't tell whether this defines the answer.

'busy gent healthier to' is the wordplay.
'busy' is an anagram indicator.
'gent'+'healthier'+'to'='genthealthierto'
'genthealthierto' with letters rearranged gives 'IN THE ALTOGETHER'.

Can you help me to learn more?

(Other definitions for in the altogether that I've seen before include "Naked" , "wearing nothing?" , "having nothing to wear?" , "unclothed" , "barely seen" .)

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

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