The structures of K3C60 and K6C60 are refined by Rietveld analysis of high-resolution time-of-flight powder neutron diffraction data. Bond length and angle constraints are not necessary to produce chemically sensible molecular structures for the fulleride anions. The results suggest loss of the distinction between single and double bonds on the fullerene molecule on reduction and are consistent with recent ab initio calculations. A simple chemical interpretation of the observed trends is given.