Despite the growing interest in immigrant integration in a wide range of scholarly literature, there is less interest in how integration might be understood by the public. Using a survey-embedded conjoint experiment in the Netherlands and the UK, we ask the public what they think constitutes successful immigrant integration. We show that the public has a multidimensional view of integration, which goes beyond a simple preference for cultural assimilation. We discover that there is a remarkably stable hierarchy of preference of integration outcomes, which is a matter of wide spread consensus in both our countries among different social groups and people with different attitudes on immigration. Using the British data we also show an integration penalty for immigrants of non-white origins. Our article places public opinion of immigrant integration at the heart of a rapidly expanding research agenda into the social and political impacts of immigration.