Delete duplicates with PostgreSQL using USING

Consise way to delete duplicates (depending on a condition, e.g. col1 and col2 being equal) while keeping the row with the highest id:

DELETE FROM
          my_table delete
    USING my_table check
  WHERE
        delete.id < check.id
    AND delete.col1 = check.col1
    AND delete.col2 = check.col2