Most scientific imaging applications of CCDs require low noise and high charge transfer efficiency. These attributes have been exhibited in devices produced by a number of manufacturers, but not all perform well as x-ray imaging spectrometers. This application requires that all charge liberated by an x-ray photon be completely collected within the original pixel. Processes of charge diffusion may prevent this from occurring and degrade the obtainable energy resolution. Measurements of charge diffusion and its effect on x-ray performance are presented for three types of English Electric Valve Co. (EEV) CCDs. These are fabricated on bulk and epitaxial wafers with resistivities of 1000 and 1011 cm. A range of different pixel sizes is employed. Measurements of detection efficiency are compared with predictions of a theoretical charge-diffusion model. Implications for optimizing the CCD structure for use in an x-ray astronomical spectroscopy application are noted.