The significance of discussion in mathematics classes has been prominently debated in the research literature. Different studies have stressed the importance of teacher flexibility in orchestrating the discussion. We introduce an operational definition of teacher flexibility. In a case study with one secondary-school mathematics teacher, we microanalyzed discussion situations in which the teacher had to change her plan according to unforeseen student replies. The analysis was aimed at characterizing situations in which the teacher was either flexible or inflexible in her interactions with students and describing the factors that affected her flexibility. We suggest four basic patterns of teacher flexibility and discuss the complexity of the factors that shape them.