We address the moral importance of fish, invertebrates such as crustaceans, snails and insects, and other animals about which there is qualified scientific uncertainty about their sentience. We argue that, on a sentientist basis, one can at least say that how such animals fare make ethically significant claims on our character. It is a requirement of a morally decent (or virtuous) person that she at least pays attention to and is cautious regarding the possibly morally relevant aspects of such animals. This involves having a moral stance, in the sense of patterns of perception, such that one notices such animals as being morally relevant in various situations. For the person who does not already consider these animals in this way, this could be a big change in moral psychology, and can be assumed to have behavioural consequences, albeit indeterminate. Character has been largely neglected in the literature, which focuses on act-centred approaches (i.e. that the evidence on sentience supports, or does not support, taking some specific action). We see our character-centred approach as complementary to, not superior to, act-centred approaches. Our approach has the advantage of allowing us to make ethically interesting and practically relevant claims about a wider range of cases, but it has the drawback of providing less specific action guidance.