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Density modification is a standard technique in macromolecular crystallography that can significantly improve an initial electron-density map. To obtain optimal results, the initial and density-modified map are combined. Current methods assume that these two maps are independent and propagate the initial map information and its accuracy indirectly through pre­viously determined coefficients. A multivariate equation has been derived that no longer assumes independence between the initial and density-modified map, considers the observed diffraction data directly and refines the errors that can occur in a single-wavelength anomalous diffraction experiment. The equation has been implemented and tested on over 100 real data sets. The results are dramatic: the method provides significantly improved maps over the current state of the art and leads to many more structures being built automatically.

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