The discovery of unusual nanorod precipitates in bismuth ferrite doped with Nd and Ti is reported. The atomic structure and chemistry of the nanorods are determined using a combination of high angle annular dark field imaging, electron energy loss spectroscopy, and density functional calculations. It is found that the structure of the BiFeO3 matrix is strongly modified adjacent to the precipitates; the readiness of BiFeO3 to adopt different structural allotropes in turn explains why such a large axial ratio, uncommon in precipitates, is stabilized. In addition, a correlation is found between the alignment of the rods and the orientation of ferroelastic domains in the matrix, which is consistent with the system's attempt to minimize its internal strain. Density functional calculations indicate a finite density of electronic states at the Fermi energy within the rods, suggesting enhanced electrical conductivity along the rod axes, and motivating future investigations of nanorod functionalities.