We consider a natural extension of the Minimal Dark Matter scenario where Dirac and Majorana SU(2)_L multiplets couple together via the Higss. We classify and study in a systematic way all the few possible models consistent with the absence of Landau poles up to very high scale, including the results for Direct Detection, and the Sommerfeld-enhanced annihilation. We demonstrate that, at freeze-out, a well educated estimation of the size of the Sommerfeld corrections can be done in the unbroken SU(2)_L limit. This is shown explicitly for the cases not present in
previous works on the subject.