The present invention provides improved methods for fabricating compound-material wafers, in particular a silicon on insulator type wafer. The improved methods lead to reduced numbers of deflects arising on or near the periphery of the wafers. In a first method, wafers are selected in dependence on edge roll off values determined at about 0.5-2.5 mm away from the edge of the wafer, where edge roll off values are determined in dependence on the second derivative of the wafer height profiles. In a second method, wafers selected according to the first method are further processed by bonding, forming a splitting layer, and detaching the two wafers at the splitting layer.