  Motivated by their appearance as Coulomb branch geometries of Class S
theories, we study the image of the local Hitchin map in tame Hitchin systems
of type-D with residue in a special nilpotent orbit $\mathcal{O}_H$. We
describe two important features which distinguish it from the type A case
studied in arXiv:2008.01020. The first feature, which we term even type
constraints, arise iff the partition label $[\mathcal{O}_H]$ has even parts. In
this case, our Hitchin image is non-singular and thus different from the one
studied by Baraglia and Kamgarpour. We argue that our Hitchin image always
globalizes to being the Hitchin base of an integrable system. The second
feature, which we term odd type constraints, is related to a particular finite
group $\overline{A}_b(\mathcal{O}_H)$ being non-trivial. When this finite group
is non-trivial, we have $\mid \overline{A}_b \mid$ choices for the local
Hitchin base. Additionally, we also show that the finite group
$\overline{A}_b(\mathcal{O}_H)$ encodes the size of the dual special piece.
