  We explore an extension of the Inert Doublet Model which allows also for CP
violation in the Higgs sector. This necessitates two non-inert doublets. The
lightest neutral scalar of the inert doublet is a candidate for dark matter.
Scanning over parameters we preserve the abundance of the dark matter in
agreement with the WMAP data. We also impose all relevant collider and
theoretical constraints to determine the allowed parameter space for which both
the dark matter is appropriate and CP is violated. In addition we find regions
where the cut-off of the model originating from naturality arguments can be
substantially lifted compared to its Standard Model value, reaching 2-3 TeV.
