  The dramatic increase in sensitivity, spectral coverage and resolution of
radio astronomical facilities in recent years has opened new possibilities for
observation of chemical differentiation and isotopic fractionation in
protostellar sources to shed light on their spatial and temporal evolution. In
warm interstellar environments, methanol is an abundant species, hence spectral
data for its isotopic forms are of special interest. In the present work, the
millimeter-wave spectrum of the $^{13}$CH$_3$OD isotopologue has been
investigated over the region from 150$-$510 GHz to provide a set of transition
frequencies for potential astronomical application. The focus is on two types
of prominent $^{13}$CH$_3$OD spectral groupings, namely the $a$-type
$^qR$-branch multiplets and the $b$-type $Q$-branches. Line positions are
reported for the $^qR(J)$ clusters for $J = 3$ to 10 for the $v_{\rm t} = 0$
and 1 torsional states, and for a number of $v_{\rm t} = 0$ and 1 $^rQ(J)$ or
$^pQ(J)$ line series up to $J = 25$. The frequencies have been fitted to a
multi-parameter torsion-rotation Hamiltonian, and upper level excitation
energies have been calculated from the resulting molecular constants.
