The group PLo(I)PLofo(I) of piecewise linear orientation preserving homeomorphisms of the unit interval, equipped with composition, has a rich array of finitely generated subgroups. A basic question one can ask is when one of these groups embeds into another. One group which seems to play a particularly important role in this quasi-order is Richard Thompson's group FF. For instance it is conjectured that every finitely generated subgroup of PLo(I)PLofo(I) either contains a copy of FF or else embeds into FF. I will describe a general dynamical criterion for when a subgroup of PLo(I)PLofo(I) does not embed into FF which covers all known examples. This is joint work with James Hyde.