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Empirical corrections for the preferred orientation of grains in powder specimens have been generalized. Treatment of asymmetric diffraction geometries [Seemann-Bohlin (Guinier) geometry; glancing-angle geometry] is included. Inclined textures (in which the maximum of the pole density of preferentially oriented planes is declined from the direction of the diffraction vector) can be also treated. The distribution function of the poles of preferentially oriented planes does not need to be axially symmetric even in the case of inclined textures. Rapid spinning around one axis is needed in this case. The texture-correction procedure has been implemented in the computer program DBWS-9006PC for Rietveld refinement.