X-ray free-electron lasers (XFELs) have inspired the development of serial femtosecond crystallography (SFX) as a method to solve the structure of proteins. SFX datasets are collected from a sequence of protein microcrystals injected across ultrashort X-ray pulses. The idea behind SFX is that diffraction from the intense, ultrashort X-ray pulses leaves the crystal before the crystal is obliterated by the effects of the X-ray pulse. The success of SFX at XFELs has catalyzed interest in analogous experiments at synchrotron-radiation (SR) sources, where data are collected from many small crystals and the ultrashort pulses are replaced by exposure times that are kept short enough to avoid significant crystal damage. The diffraction signal from each short exposure is so 'sparse' in recorded photons that the process of recording the crystal intensity is itself a reconstruction problem. Using the EMC algorithm, a successful reconstruction is demonstrated here in a sparsity regime where there are no Bragg peaks that conventionally would serve to determine the orientation of the crystal in each exposure. In this proof-of-principle experiment, a hen egg-white lysozyme (HEWL) crystal rotating about a single axis was illuminated by an X-ray beam from an X-ray generator to simulate the diffraction patterns of microcrystals from synchrotron radiation. Millions of these sparse frames, typically containing only ∼200 photons per frame, were recorded using a fast-framing detector. It is shown that reconstruction of three-dimensional diffraction intensity is possible using the EMC algorithm, even with these extremely sparse frames and without knowledge of the rotation angle. Further, the reconstructed intensity can be phased and refined to solve the protein structure using traditional crystallographic software. This suggests that synchrotron-based serial crystallography of micrometre-sized crystals can be practical with the aid of the EMC algorithm even in cases where the data are sparse. © 2016 Jennifer L. Wierman et al.