Demai, Chapter Six, Mishnah Three
This mishnah and the next deal with scenarios where priests or Levites rent fields from Israelites or vice versa. The question that needs to be answered is, since the priests get the terumah in any case and the Levites the tithe, do they still split this part of the produce evenly?
1) A priest or a Levite who rented a field from an Israelite [for a share in the produce], just as they divide the non-sacred produce, so they divide the terumah.
2) Rabbi Eliezer says: the tithes belong to them (the tenants), for they entered the field with this expectation.
Section one: In this scenario the field belongs to an Israelite and he rents it out to a priest or a Levite in return for a set share in the produce. The mishnah rules that they divide all of the produce according to the plan, even the terumah and tithes that will eventually be separated. In other words, the priest or Levite cannot say to the Israelite that they should first take all of the terumah or tithes and then split with him the rest of the produce. When the Israelite separates the terumah and tithes later, he may give them to any priest or Levite he so desires.
This section only mentions terumah and not tithes because terumah is the opposite of non-sacred produce (hullin). The rule is the same for tithes.
Section two: Rabbi Eliezer says that the tithes and terumah are first taken by the tenants, the priest and the Levite because they would have rented the field assuming that they were going to keep the terumah and tithes for themselves. Since we assume that they rented the field with this in mind and the terumah and tithes will in any case be given to some priest and Levite, this priest or Levite can keep the terumah or tithes for himself.
Albeck explains that this section mentions only tithes because tithes is a term that can include terumah. We should note that by mentioning tithes in this section and terumah in the first the mishnah is balanced, including both without having to mention both twice, which would have been more clumsy.