  We present a version of the Type II Seesaw mechanism for parametrically small
Dirac neutrino masses. Our model starts from an $\text{SU}(2)_\text{L} \otimes
\text{SU}(2)'\otimes \text{U}(1)_\text{X}$ gauge extension of the Standard
Model involving a sector of mirror fermions. A bidoublet scalar with a very
small vacuum expectation value connects the SM leptons with their mirror
counterparts and we can identify the mirror neutrino with the right-handed
neutrino. Similar to the conventional Type II Seesaw, our particle spectrum
features singly- and doubly-charged scalars. The strong CP problem is solved by
a discrete exchange symmetry between the two sectors that forces the
contributions of quarks and mirror quarks to the strong CP phase to cancel each
other. We discuss the low-energy phenomenology, comment on the cosmological
implications of this scenario and indicate how to realize successful Dirac
leptogenesis.
