One who sleeps under the bed in the succah has not fulfilled his obligation [to sleep in a succah].  R’ Yehudah said: We regularly slept under the bed in the presence of the Elders and they said nothing to us.  R’ Shimon said: There is a case of Tavi, Rabban Gamliel’s slave, who used to sleep under the bed. Rabban Gamliel said to the Elders, “Have you observed my slave Tavi? He is a scholar and knows that [gentile] slaves are exempt from [the obligation of] succah —- that is why he sleeps under the bed.” And incidentally we deduced that one who sleeps under the bed does not fulfill his obligation [to sleep in a succah].

If one supports his succah on the legs of a bed, it is valid. R’ Yehudah says: If it cannot stand by itself it is invalid.  A disarranged succah, or one whose shade[d area] is greater than its sun[lit area], is valid. [If the succah] is thickly covered like a house, even though the stars cannot be seen from inside it, it is valid.