The phrase "with a head on" is used to describe someone who is level-headed and able to make clear decisions. Synonyms for this phrase include "calm-headed," "clear-thinking," "rational," "composed," and "sober-minded." These words can be used to describe someone who is able to approach a situation with a cool and collected attitude, rather than getting carried away by emotions or stress. This type of person is often seen as reliable, trustworthy, and capable of handling difficult situations with grace and poise. Whether you are describing yourself or someone else, using these synonyms can help to paint a clear picture of someone who is able to stay focused and remain calm under pressure.