A convex spinal fusion interbody space device includes spaced apart superior and inferior abutment surfaces which are effectively medially convex. The peak of such convexity is displaced anteriorly of a central plane through the device. The spacer device has a height which is greater than the width of the device. The spacer device is implanted between a pair of adjacent vertebrae by insertion in a tipped-over orientation and then reoriented to an upright orientation for engagement by facing surfaces of the vertebrae. Fusion promoting bone material is packed between the vertebrae and about and within the spacer device subsequent to implantation.