If you are clear-headed, your mind is working well. You can think in a straight line, notice what matters, and make a sensible choice. People reach for this word when the moment is messy or emotional: a clear-headed person does not get swept away. You also hear it after illness, tiredness, or drink — they are clear-headed again when the fog has gone. It is a kind, slightly careful way to praise someone's thinking. Though actually, it is not the same as clever. You can be very smart and still not clear-headed, if feelings or hope are doing the deciding. It is about being steady and not confused.