In this paper, I describe progress in research designed to explore the effect of the combination of behavioral and visual fidelity of avatars on users' social presence in synchronous and emotionally engaged mobile phone communication. I specifically focus on ways to secure mobile phone users' anonymity while preserving their most important nonverbal affective behaviors. The research measures social presence in several dimensions, and investigates the impact of combinations of behavioral and iconic realism of avatars on the measures. Keywords Mobile phone communication, avatar realism, anonymity, affective behavior, social presence ACM Classification Keywords H.5.m. Information interfaces and presentation (e.g., HCI): Miscellaneous; J.4 Computer Applications: Social and Behavioral Sciences---Psychology.