  We consider the case of coherent gauge invariant operators in the SU(3) and
SO(4) sectors. We argue that in many cases, these sectors can be closed in the
thermodynamic limit, even at higher loops. We then use a modification of the
Bethe equations which is a natural generalization of a proposal put forward by
Serban and Staudacher to make gauge theory predictions for the anomalous
dimensions for a certain class of operators in each sector. We show that the
predictions are consistent with semiclassical string predictions at two loops
but in general fail to agree at three loops. Interestingly, in both cases there
is one point in the configuration space where the gauge theory and string
theory predictions agree. In the SU(3) case it corresponds to a circular string
with R-charge assignment (J,J,J).
