  We study the dispersion of the magnons (triplet states) in
SrCu$_2$(BO$_3$)$_2$ including all symmetry-allowed Dzyaloshinskii-Moriya
interactions. We can reduce the complexity of the general Hamiltonian to a new
simpler form by appropriate rotations of the spin operators. The resulting
Hamiltonian is studied by both perturbation theory and exact numerical
diagonalization on a 32-site cluster. We argue that the dispersion is dominated
by Dzyaloshinskii-Moriya interactions. We point out which combinations of these
anisotropies affect the dispersion to linear-order, and extract their
magnitudes.
