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In this paper the anisotropy of anomalous scattering at the Br K-absorption edge in brominated nucleotides is investigated, and it is shown that this effect can give rise to a marked directional dependence of the anomalous signal strength in X-ray diffraction data. This implies that choosing the correct orientation for crystals of such molecules can be a crucial determinant of success or failure when using single- and multiple-wavelength anomalous diffraction (SAD or MAD) methods to solve their structure. In particular, polarized absorption spectra on an oriented crystal of a brominated DNA molecule were measured, and were used to determine the orientation that yields a maximum anomalous signal in the diffraction data. Out of several SAD data sets, only those collected at or near that optimal orientation allowed interpretable electron density maps to be obtained. The findings of this study have implications for instrumental choices in experimental stations at synchrotron beamlines, as well as for the development of data collection strategy programs.