These [items] are obligated in challah but are exempt from tithes: leket, shich'chah, pe'ah, ownerless [produce], maaser rishon whose terumah was taken, maaser sheni and hekdesh [produce] that were redeemed, the leftover of the omer, and grain which has not attained a third [of its growth]. R' Eliezer says: Grain which has not attained a third [of its growth] is exempt from challah.