The technique of coherent X-ray diffraction imaging (CXDI) has recently shown great promise for the study of inorganic nanocrystals. In this work the CXDI method has been applied to the study of micrometer-size protein crystals. Finely sampled diffraction patterns of single crystals were measured and iterative phase-retrieval algorithms were used to reconstruct the two-dimensional shape of the crystal. The density maps have limited reproducibility because of radiation damage, but show clear evidence for crystal facets. Qualitative analysis of a number of single-crystal diffraction peaks indicates the presence of inward surface contraction on 2 microm size crystals. A survey of several hundred diffraction patterns yielded a number of examples with dramatic single-sided streaks, for which a plausible model is constructed.