The term 'smoothly polite' can be described by two crossword solutions: 'URBANE' (6 letters) and 'SUAVE' (5 letters). URBANE is an adjective that means having the polish and suavity regarded as characteristic of sophisticated social life in major cities. SUAVE is an adjective that means having a sophisticated charm and grace. Both words imply politeness and good manners, but with a certain level of sophistication.