  We analyze S-duality of orientifolds of the Calabi-Yau cone over the first
del Pezzo surface ($dP_1$). The S-duals of known phases, described by quiver
gauge theories, contain intrinsically strongly-coupled sectors. These sectors
are realized by a higher multiplicity intersection of NS5 branes and D5 branes
atop an O5 plane, and can be thought of as stuck at the infinite coupling point
between two Seiberg-dual gauge theories. We argue that such sectors appear
generically in orientifolds of non-orbifold singularities, where in many
examples every orientifold phase contains such a sector. Understanding such
sectors is therefore key to understanding orientifolds of Calabi-Yau
singularities. We construct the strongly-coupled sectors for $dP_1$
orientifolds using deconfinement, and show that they have interesting,
non-trivial properties. Using this construction, we verify the predictions of
S-duality for $dP_1$.
