What are the requirements for Once-returner? I know about the ten fetters model. I read that a Once-returner has very reduced desire and aversion to the point that they only appear when tired or unmindful. 

Are there other relevant requirements?

Are there stuff that hint that the person is or is not a Once-returner? For example, if the person doesn't reach jhana, does that HINT that maybe he is not a Once-returner?
The once returner just destroys the 3 fetters and reduce lusts


  Again, Sāriputta, consider the person who is accomplished in the precepts, but not in concentration, nor in wisdom — by destroying the
  three fetters and reducing lust, hatred and delusion, he becomes a
  Once-returner, who returns to this world again once only and makes an
  end of ill.
  
  This, Sāvatthi, is the sixth person, who, dying with some attached
  remainder, is altogether freed from hell, rebirth in the womb of an
  animal, the realm of ghosts, from the untoward way, the ill way, the
  abyss, hell.


http://obo.genaud.net/dhamma-vinaya/pts/an/09_nines/an09.012.hare.pts.htm#p1

Apparently the first people who are ''moderately'' good at concentration are the ''Clan-to-clan-goer''