Related su Pe'ah 8:6

We do not reduce [the agricultural gifts] to the poor during the years of of the poor person's tithe (i.e., the third and sixth years of the agricultural cycle) to less than half a kav of wheat or a kav of barley (Peah 8:5). In what context does this apply? [For grain that has been brought in to] the threshing floor, but [for grain brought] inside his house, we give [the poor person] any amount (כל שהו not כל שדהו), and we are not concerned [that it is too little]. And [similarly for] the remainder of the priestly gifts and the [gifts for the] Levite, we give any amount, and we are not concerned [that it is too little]. [If he is saving some to give to his poor relatives, see Peah 8:6], he can save half and give half. Abba Yosa ben Dostai said in the name of Rabbi Eliezer, "[If he] wants, he [can] place before [the poor people] a third and retain two-thirds for his [poor] relatives."