An exhaustive new report on the nation’s top 472 occupations finds that immigrants — legal or not — take some jobs from Americans, dispelling the accepted view that foreign workers only fill jobs Americans don’t want to do.

The study based on U.S. census data from 2009 to 2011 found that of the 472 jobs, immigrant workers outnumber “native-born” Americans in only six occupations: sewing machine operator, agriculture, masonry, plasterer, fruit and vegetable sorter, and tailor.