We examine lateralization of lateral displays in convict cichlids, Amatitlania nigrofasciata , and show a population level preference for showing the right side. This enables contesting pairs of fish to align in a head-to-tail posture, facilitating other activities. We found individuals spent a shorter mean time in each left compared with each right lateral display. This lateralization could lead to contesting pairs using a convention to align in a predictable head-to-tail arrangement to facilitate the assessment of fighting ability. It has major implications for the common use of mirror images to study fish aggression, because the ‘opponent’ would never cooperate and would consistently show the incorrect side when the real fish shows the correct side. With the mirror, the ‘normal’ head-to-tail orientation cannot be achieved.