* Tower-like: Tiferet Yisrael (Yachin [[Sukkah]] 3:6) writes that ideally, the etrog should be like a tower, meaning thick at the bottom and thin on top. Nitei Gavriel (p. 140) and Arbaat Haminim Lamedharim (p. 252) agree.
* Symmetrical: Tiferet Yisrael (Yachin Sukkah 3:6) writes that ideally, the pitom should be lined up with the oketz. [[Kashrut]] Arbaat Haminim (p. 8) agrees. Arbaat Haminim Lamehadrin (p. 177) cites Rav Nissim Karelitz, who says that this criterion is met if the pitom and oketz are approximately lined up.
* Aesthetic beauty: Chazon Ovadia (p. 278) quotes the Maamar Mordechai, who asserts that besides for the properties that Chazal specified, the beauty of an etrog depends on the subjective view of the individual. Accordingly, Rabbi Mordechai Willig (quoted by Rabbi Eliakim Koenigsberg . min. 44-6) would ask his wife to pick the nicest-looking etrog from amongst the valid etrogim.</ref>
# A grafted Etrog is pasul whether it was grafted with lemon, promerance, or any other fruit. <Ref>The overwhelming consensus of Achronim hold that a grafted Etrog is unfit all days of [[Sukkot]] and one may not make a Bracha on it. These Achronim include Magen Avraham 648:23, Taz 648:3, S”A HaRav 648:31, Mishna Brurah 648:65, Chazon Ovadyah [[Sukkot]] (pg 223).</ref>
# Even if the Etrog is only in doubt one may not make a Bracha on the Etrog. <Ref> Chazon Ovadyah [[Sukkot]] (pg 228-232), Sh”t Mishneh Halachot 6:117 </ref>
# If one has an etrog that’s safek if it’s grafted and an etrog that’s not as hadar (“beautiful”), one should make the Bracha on the true etrog first and after shaking the minim with it, one should take the one that’s a safek grafted. <Ref> The Achronim quote the story of when the Grach (Rav Chaim Soloveitchik) had an etrog that was safek grafted and one that’s surely non-grated but not as hadar. The made the Bracha on the safek grafted one so that he could fulfill his mitzvah with the more hadar etrog, rather than use the true etrog and once he fulfills the mitzvah he would no longer be able to fulfill the mitzvah of hadar. However, the Mikrei Kodesh ([[Sukkot]] 2:9) and Chazon Ovadyah [[Sukkot]] (pg 244) argue that shaking the safek kasher one first would be a safek [[hefsek]] between the bracha and shaking on the true etrog and so one should take the true etrog first. </ref>
# An Etrog which is so dry that it doesn't have any moisture is invalid. <Ref>S”A 648:1 writes that a dry Etrog which has no moisture is invalid.</ref>
# It is possible to check if an Etrog is invalid by piercing it with a needle with a string attached and if there's moisture on the string the Etrog is not considered dry. In order that this procedure not make the Etrog invalid because of a hole, one should pierce the thick part of the Etrog without piercing the Etrog completely through and through, others suggest that one should pierce it along the length of the Etrog. <ref> The S”A 648:1 writes that one could check whether an Etrog is considered dry by piercing it with a needle that has a string attached and if the string comes out moist the Etrog is considered moist. The Mishna Brurah 648:3 quotes a dispute regarding how to do this procedure without invalidating the Etrog by having a hole in it. Some say that one should make a hole in the thick part of the Etrog so that its not a hole through and through. Others say that one should make a hole along the length of the Etrog, along the Uketz-Chotam axis. </ref>