It has been argued that the higher a country’s ethnic heterogeneity, the higher the reluctance of the (normally) richer ethnic majority to redistribute toward the (normally) poorer ethnic minority. We analyze experimentally how preferences for redistribution vary in the presence of ethnic heterogeneity. We ask a representative sample of German citizens to decide how much money to redistribute from a German citizen to a recipient who could either be another German citizen, an asylum seeker, or an economic migrant. Discrimination is large, as German recipients receive significantly higher transfers than foreign recipients. Asylum seekers are less discriminated against than economic migrants. We analyze patterns of redistribution when recipients hold attributes that may be deemed as desirable, i.e., holding a university degree and performing voluntary community work. While holding a university degree does not increase transfers, recipients performing community work receive significantly higher transfers than others. While the premium for holding a desirable attribute is generally not significantly different for Germans and foreigners, discrimination for asylum seekers tends to go close to zero when they hold desirable attributes. Conversely, discrimination remains sizeable for economic migrants. Participants on the right wing of the political spectrum react significantly to migrants holding desirable attributes. These results suggest that the policy of many immigration systems of conditioning entry to migrants holding university degrees may not reduce discrimination significantly.