  We summarize the known obstructions to subfactors with principal graphs which
begin with a triple point. One is based on Jones's quadratic tangles
techniques, although we apply it in a novel way. The other two are based on
connections techniques; one due to Ocneanu, and the other previously
unpublished, although likely known to Haagerup.
  We then apply these obstructions to the classification of subfactors with
index below 5. In particular, we eliminate three of the five families of
possible principal graphs called "weeds" in the classification from
arXiv:1007.1730.
