The twisted nerve (gid hanasheh): the sciatic nerve, as according to the patriarch Jacob's was damaged when he fought with an angel, cannot be eaten and is removed by nikkur.
Untithed food (tevel): produce of the Land of Israel requires the removal of certain tithes, which in ancient times were given to the Kohanim (priests), Levites and the poor (terumah, maaser rishon and maaser ani respectively) or taken to the Old City of Jerusalem to be eaten there (maaser sheni).