Holiday season flights?

[jamduf]

I am trying to book out of the US with award miles on United during the holidays. I want to come back somewhere between Jan 3-6 2014. They do not  even show any flts on those return dates. Is that because they are already booked full and I missed out. I can get Flts for a couple weeks over Christmas but I would miss new years over there. Should I wait and see if they add flts for early Jan. or grab the xmas one that I can get before its gone and look to book earlier next year to get the new years for 2015?

[LASportsNut]

Try EVA as they are part of the same reward program now.  I am flying from LAX in Nov return in Dec for $1013.