When it comes to choosing tasks, values can have a significant impact. This study explores teachers' values as they choose one task from among three that they believe will have the most potential to occasion mathematical creativity in the classroom. Participants' analyses of each task, as well as their reasons for choosing one task as most preferred, were analyzed in terms of task features and cognitive demands, as well as their explicit reference to fluency, flexibility, and originality. Two values shared by most participants were having several solution paths and a task that would challenge students. Of particular interest are task features and cognitive demands that were associated with a task at the initial stage of analysis but were not mentioned as a reason for choosing that task as occasioning mathematical creativity. Dilemmas and challenges regarding the study of values are discussed.