Abstract: A widespread view among philosophers is that the maximum potential for positive welfare of individuals with sophisticated cognitive capacities (like human persons) is significantly higher than that of individuals without those capacities (like most non-human animals). A less common, but influential view, is that the effect of sophisticated cognitive capacities is not symmetrical, in the sense that the maximum potential for negative welfare is comparable between individuals with and without those capacities. In this article I challenge the latter view (which I call the Welfare Asymmetry Thesis) by arguing that persons do have a maximum potential for negative welfare that is significantly higher than that of animals. I contend that this is plausible even when viewed from different theories of welfare. After addressing some potential replies that a defender of Welfare Asymmetry Thesis might make, I conclude by briefly discussing two implications of my proposal: that it can provide support to the conventional practice of granting persons more protections from welfare-reducing events than to animals, and that it can undermine the widespread view that the lives of persons matter more than the lives of animals.