The phrase "making off top one's head" generally means to come up with something quickly without much thought or preparation. Antonyms for this phrase would include "deliberate," "planned," "calculated," and "intentional," all of which imply a more systematic approach. Other potential antonyms might include "meticulous," "careful," "thoughtful," and "analytical," since these terms all suggest a more thoughtful, detail-oriented approach to problem-solving or decision-making. Ultimately, the opposite of "making off top one's head" is any approach that involves careful consideration, thorough research, and a willingness to take the time to come up with well-thought-out solutions.
