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Diffractive beam-splitting elements are typically designed for replicating beams on positions belonging to an equidistant grid in the spatial spectrum. The parameter of the output grid follows directly from the period of the beam-splitter transmission through the grating equation. Our objective is to develop design strategies allowing a more accurate positioning of the replicated beams. Issues occurring when the output grid parameter is decreased below the output beam width are discussed and shown to be avoidable. Furthermore, a design algorithm is introduced, which permits an arbitrary positioning of the replicated beams. This algorithm is constructed for high computational efficiency by utilizing fast Fourier transform operations in the major part of its iterations.