Going beyond simplified models is key to combining the results of the many different experimental probes of Dark Matter (DM). To this end, a basis of Minimal Consistent Dark Matter (MCDM) models should be gauge-invariant, renormalisable and anomaly-free. We perform a systematic study of such viable MCDM models which may be constructed by the addition of a single non-chiral weak SU(2) multiplet of fermions (either Dirac or Majorana). We consider the case where only SM fields play the role of the mediator, and extend to include an additional mediator multiplet which may be scalar,fermion or vector. The fermion multiplet should be odd under a stability preserving discrete symmetry, but the mediator may be odd or even. We explore the phenomenology of a representative model, a two-component dark-sector containing a Dirac fermion alongside a Z2 even scalar with only bi-linear couplings to SM, which may itself be accidentally stable.