Many animals use coloration to signal dominance and fighting ability. In birds, plumage coloration is often linked to individual quality, but less research has investigated coloration in unfeathered traits (i.e. ‘bare parts'), despite theoretical expectations that they might be more reliable signals. Here, we investigate the relationship between multiple ornaments and social dominance in a wild population of the cooperatively breeding Australian Swamphen (known locally as and hereafter referred to as Pūkeko; Porphyrio melanotus melanotus) to test the hypothesis that bare-part ornaments should be more strongly correlated with dominance than plumage coloration. We show that the size and color of the pūkeko's frontal shield (a bare-part ornament), as well as the brightness and chroma of the blue-UV breast plumage, are correlated with social dominance in adult birds. However, the correlation between frontal shield size and dominance was much higher than that between plumage color and dominance, and was also higher than most previously published correlations between plumage traits and dominance. Additionally, frontal shield size, but not breast coloration, was correlated with the size of the testes in male pūkekos, which may be because bare-part ornaments are more closely tied to an individual's current physiology than plumage ornaments. While correlative, our results demonstrate that bare-part and plumage traits could act as redundant ornaments, but with differing reliability, and suggest that future studies on bare-part ornaments will enhance our understanding of dominance signaling.