(Mishnah): One can always give Peah (even after he has harvested) and the produce is exempt from Maaseros until the pile has been smoothed over.

(R. Akiva): And he may take (seeds) from the granary and sow and it is exempt from Maaseros until smoothed. He made feed it to an animal, a beast or a bird and it is exempt from Maaseros until smoothed.

If a Kohen or Levi bought produce from the granary before it was smoothed, they may keep the Maaseros. One who consecrated his produce and then redeemed it (from the treasurer) before it was smoothed, it is obligated in Maaseros until the treasurer smoothed it.

(Gemara) (R. Yosi b'R. Yaakov b'R. Zavdi citing R. Abahu/ R. Nechemia bar Ukvan): (The Mishnah in Bikurim teaches that) if a person declared something Bikurim after the pile was smoothed, it is exempt from Terumos and Maaseros (as the obligation of Bikurim preceded them).

Support (R. Chagai to R. Yosi): (Baraisa) 'One can always give Peah (even after he has harvested) and the produce is exempt from Maaseros until the pile has been smoothed over.' This shows that if he gave Peah after it was smoothed, it is obligated in Maaseros. The Baraisa then added 'which is not the case for Bikurim' (which we assume to mean that they are exempt from Terumos and Maaseros even after smoothing).

Rebuttal: Perhaps the Baraisa is in fact saying that Bikurim are even obligated in Terumos and Maaseros before smoothing.

(Mishnah in Terumos): Why are first-fruits called 'Bikurim'? Because they precede everything else (such as separating Terumah). Whatever is listed first in the pesukim of tithes must be separated first; so that, for example, Terumah produce is not obligated in Maaser Rishon, but Maaser Rishon is obligated in Terumah (if it wasn't separated earlier, since it follows Terumah in the pesukim).

(When the Mishnah taught that one can always give Peah - even after he has harvested; which implies that even if he gave it when it was still attached, if he would give more after harvesting, it would be exempt from Maaseros) it is the view of Beis Shammai, (that even though the Peah is not valid, it is exempt from Maaseros because it became Hefker (ownerless)) - Beis Shammai hold that when one makes something ownerless just for the poor, it is valid.