The molecular-replacement equations, in which electron-density averagi
ng and skew averaging have been unified, were used in reciprocal space
to refine and extend the resolution of phased reflections. A procedur
e has been developed for the treatment of molecular envelopes of gener
al shape. The equations were successfully applied to the reflection da
ta of bacteriophage phi X174 (60-fold redundancy). Truncation of the G
diffraction function beyond the first few nodes did not have a signif
icant effect on the quality of the molecular-replacement equations. Re
ciprocal-space molecular-replacement averaging should prove to be a us
eful alternative to real-space averaging. Strategies are discussed tha
t are possible only in reciprocal space.