There are many synonyms for the word "straight-faced." Some of the most commonly used include "serious," "stern," "unsmiling," "expressionless," "deadpan," and "stone-faced." Each of these words conveys a sense of emotionlessness or seriousness, and can be used to describe someone who is not showing any visible signs of emotion or humor. Other potential synonyms for "straight-faced" might include "stoic," "impassive," "unreadable," or "blank-faced." Ultimately, the choice of which synonym to use will depend on the specific context and tone of the writing, as well as the intended audience and purpose of the text.