"Make up the top of one's head" is an idiomatic expression that refers to giving an immediate or impromptu answer without much thought or research. Antonyms for this expression would include well-researched, prepared, thought-out, planned, and calculated. For instance, if someone is asked to make up the top of their head for what changes they would want to see in their community, they may offer a quick and hasty response. However, if they were to take the time to research the matter and plan their answer, their response would be well-reasoned, well-informed, and thoroughly considered. Taking the time to prepare and plan can help them arrive at a more satisfactory response.