What explains variation in individuals' opposition to immigration? While scholars have consistently shown cultural concerns to be strong predictors of opposition, findings regarding the labor-market competition hypothesis are highly contested. To help understand these divergent results, we distinguish between the prevalence and conditional impact of determinants of immigration attitudes. Leveraging a targeted sampling strategy of high-technology counties, we conduct a study of Americans' attitudes toward H-1B visas. The plurality of these visas are occupied by Indian immigrants, who are skilled but ethnically distinct, enabling us to measure a specific skill set (high technology) that is threatened by a particular type of immigrant (H-1B visa holders). Unlike recent aggregate studies, our targeted approach reveals that the conditional impact of the relationship in the high-technology sector between economic threat and immigration attitudes is sizable. However, labor-market competition is not a prevalent source of threat and therefore is generally not detected in aggregate analyses.