 If justice requires equality only by default, it might seem to apply only in a narrow range of cases. How could egalitarian justice be made more robust? One approach involves declaring a wider range of factors irrelevant to just distribution. Thus one formulation of the principle holds that no-one should be worse-off than anyone else as a result of their ‘morally arbitrary’ characteristics, where a characteristic is morally arbitrary when its possessor cannot claim credit for having it. This captures a widespread intuition that people should not be advantaged or disadvantaged by virtue of their race or gender, but extends it (more controversially) to all personal features with a genetic basis, such as natural talents and inborn dispositions. In doing so, it discounts most claims of desert, since when people are said to deserve benefits of various kinds, it is usually for performing actions or displaying qualities that depend upon innate characteristics such as strength or intelligence. In the following section, we will see how egalitarian theories of justice have tried to incorporate some desert-like elements by way of response. But otherwise justice as equality and justice as desert appear to be in conflict, and the challenge is to show what can justify equal treatment in the face of inequalities of desert.