Sleep lightly (4)

I believe the answer is:

doze

'sleep lightly' is the definition.
(I've seen this in another clue)

This is all the clue.

(Other definitions for doze that I've seen before include "Take forty winks" , "Catnap" , "Sleep fitfully" , "Nod off" , "A short light sleep" .)

I've seen this clue in The Times, The Telegraph, The Wall Street Journal, The Mirror, The Star Tribune and The Sunday Times.

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