Recently, the fabrication of computer-generated holograms by diamond face turning with a nanometer-stroke fast tool servo (nFTS) has been demonstrated. Existing methods for the design of diamond-turned holograms account for their spiral-shaped surface topology and the fact that only the phase of a wave field can be modulated. Here we present an algorithm enabling the additional consideration of two important fabrication-related properties: the shape of the diamond tool used and the limited control frequency of the nFTS. Our method is based on the generalized projections method and enables the design of holograms for the reconstruction of arbitrary intensity distributions in the far field. Experimental results are presented, demonstrating the advantages of the method.