This paper estimates the multi-dimensional human capital endowments of immigrants by characterizing their occupational decisions. This approach allows for estimation of physical skill and cognitive ability endowments, which are difficult to measure directly. Estimation implies that immigrants as a whole are abundant in cognitive ability and scarce in experience/training and communication skills. Counterfactual estimates of the wage impacts of immigration are skewed: the largest gain from preventing immigration is 3.2% higher wages, but the largest loss is 0.3% lower wages. Crowding of immigrants into select occupations plays a minor role in explaining these impacts; occupations’ skill attributes explain the bulk.