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The control of solidification microstructure is critical to successful laser processing of single-crystal (SX) nickel-base superalloys and a practical tool for the microstructural control is processing–microstructure maps. However, the maps presented in literature do not consider the effects of powder feeding during laser additive manufacturing (LAM) of SX superalloys. This paper therefore presents a simple and feasible strategy to deal with the effects of powder feeding and to extend the combined numerical model used to calculate processing–microstructure maps. A characteristic ratio of epitaxial SX growth was defined to quantitatively compare the final solidification microstructure. Resulting processing–microstructure maps can estimate the influence of most processing variables, especially powder feeding rate, on the extent of epitaxial SX growth and the position of columnar-to-equiaxed transition. Using the processing parameters selected according to these processing–microstructure maps, a multi-layer SX deposit with fine dendrites was successfully fabricated by LAM. This successful SX LAM indicates that these new processing–microstructure maps involving powder feeding are reliable and useful because they can determine proper processing windows for LAM of SX superalloys and further advance the understanding of the processing–microstructure relationship in powder-feeding LAM process. [ABSTRACT FROM AUTHOR]