Graphene films prepared by heating the SiC(0001̅ ) surface (the C-face of the {0001} surfaces) in a vacuum or in a Si-rich environment are compared. It is found that different interface structures occur for the two situations. The former yields a well known 3 × 3 reconstructed interface, whereas the latter produces an interface with √43 × √43-R ± 7.6° symmetry. This structure is shown to contain a graphene-like layer with properties similar to the 6√3 × 6√3-R30° “buffer layer” that forms on the Si(0001) surface (the Si-face).