In a recent theoretical paper, Birsch, Schnell & Clayton (2020) introduced a multidimensional framework of animal consciousness. In two online studies, we adopted their classification system and asked which of these dimensions contribute most to moral concern for non-human beings. Participants placed moral value on mental attributes more than physical similarity to humans in biology, appearance, and size. Specifically, behavioural indications of rich and complex visual processing had strong effects on both consciousness ratings and moral concern, more so than indications of self-awareness. Furthermore, moral worth was highly correlated with consciousness ratings, across items and participants. We discuss our findings in light of the philosophical debate over the moral significance of functional aspects of consciousness (Carruthers, 2019; Danaher, 2020; Levy, 2014), and in relation to the relevance of the scientific study of consciousness to ethics.