Solar rotational tomography is applied to Large Angle and Spectrometric Coronagraph (LASCO) C2/Solar and Heliospheric Observatory (SOHO) observations covering the period 1996-2010, resulting in a set of electron density maps at a height of 4 R ☉ from which rotation rates can be calculated. Large variation of rotation rates is measured. Rates are dominated by the Carrington rotation rate (14.18 deg d–1 sidereal), but at times over the solar cycle, rates are measured between –3 and 3 deg d–1 relative to the Carrington rotation rate. Rotation rates can vary considerably between latitudes, even between neighboring latitudes. They can remain relatively stable or change smoothly over long periods of times, or can change rather abruptly. There are periods for certain latitudes (for example, the equator at solar maximum) when the movement is dominated by rapid structural reconfiguration, not a coherent rotation. These results raise new questions regarding the link between the Sun and the corona, and provide fresh challenges to interpretations of the coronal structural evolution and the development of large-scale coronal models. In particular, can interchange reconnection provide an explanation of the considerable latitudinal differences in rotation rates, and what mechanism can explain abrupt changes in rotation rates?