The paper presents a theoretical framework addressing three aspects of embodied pedagogical agents: visual static appearance, pedagogical role, and communicative style. The framework is then applied to a user study where 90 school children (aged 12-15) in a dummy multimedia program were presented with either an instructor or a learning companion condition. They were then to choose between eight visually different embodied pedagogical agents: four more naturalistic (detailed & 3D-rendered) and four more stylized (simplified & cartoonish). Finally the participants were to choose between a strictly task-oriented versus a task- and relation-oriented pedagogical agent. The goal of the study was to explore possible relations between the three aspects mentioned above with respect to user preferences. Results were: (i) when the agent was introduced as a learning companion, female students displayed a significant tendency to choose a more stylized visual character, (ii) when the agent was introduced as a learning companion, female students displayed a significant tendency to choose a task- and relation-oriented agent, and (iii) in the case when students had chosen a more stylized character, there was a significant tendency to choose a task- and relation-oriented agent. The paper also discusses limitations and strengths of the study, and advocates careful descriptions in studies of this kind--especially regarding the notion of visual realism. (Contains 13 figures, 7 footnotes, and 4 tables.)