A surgical reamer for cutting an opening in a facet joint for placement of a dowel between the sides of the facet joint to immobilize the joint and create a fusion. The reamer is used with a set of surgical instruments to prepare facet joints for insertion of dowels. The reamer creates a bone shelf above the opening for the dowel to prevent migration of the dowel. The reamer is configured with a flat profile in one plane to allow insertion into the facet joint and the profile of the dowel in the perpendicular plane to create a shape corresponding to the dowel when rotated. The neck of the reamer is smaller in diameter at the coronal end to allow creation of a bone shelf in the facet above the opening for the dowel. The bone shelf resists migration of the dowel out of the prepared opening in the facet.