  We report resonant inelastic x-ray measurements of insulating La$_2$CuO$_4$
and Sr$_2$CuO$_2$Cl$_2$ taken with the incident energy tuned near the Cu K
absorption edge. We show that the spectra are well described in a shakeup
picture in 3rd order perturbation theory which exhibits both incoming and
outgoing resonances, and demonstrate how to extract a spectral function from
the raw data. We conclude by showing {\bf q}-dependent measurements of the
charge transfer gap.
