  We study the spectrum of anomalous dimensions of short operators in planar
ABJM theory at two loops. Specifically we develop a method for solving the
OSp(6|4) Bethe ansatz equations for a certain class of unpaired length-4 states
with arbitrarily high number of excitations, and apply it to identify three new
sequences of rational eigenvalues. Results for low-lying paired states in the
OSp(4|2) sector are obtained by direct diagonalization of the spin chain
Hamiltonian. We also study the SL(2|1) sector and identify the set of states
that corresponds to the SL(2)-like Bethe ansatz of Gromov and Vieira. Finally
we extend part of our analysis to length-6 operators.
