Research on creation of virtual humans enables increasing automatization of their behavior, including synthesis of verbal and non-verbal behavior. As the achievable realism of different aspects of agent design evolves asynchronously, it is important to understand if and how divergence in realism between behavioral channels can elicit negative user responses. Specifically, in this work, we investigate the question of whether autonomous virtual agents relying on synthetic text-to-speech voices should portray a corresponding level of realism in the non-verbal channels of motion and visual appearance, or if, alternatively, the best available realism of each channel should be used. In two perceptual studies, we assess how realism of voice, motion, and appearance influence the perceived match of speech and gesture motion, as well as the agent’s likability and human-likeness. Our results suggest that maximizing realism of voice and motion is preferable even when this leads to realism mis-matches, but for visual appearance, lower realism may be preferable. (A video abstract can be found at https://youtu.be/arfZZ-hxD1Y.)