  In addition to being a solution to the little hierarchy problem, the Mirror
Twin Higgs provides a natural setting for Asymmetric Dark Matter. In its
incarnation with only one Higgs doublet and its mirror copy, dark matter would
however almost certainly consist mostly of mirror atoms, which is severely
ruled out by constraints on dark matter self-interactions. By adding a second
Higgs doublet and its mirror, the vevs of the different Higgses can be arranged
such that dark matter consists mostly of mirror neutrons, which is
cosmologically viable. In this paper, it is shown that current constraints from
colliders, flavour and cosmology can accommodate such a vev structure with
little increase in the necessary tuning.
