One of the motivating ideas behind X-ray free-electron lasers is to obtain atomic structures of biological macromolecules without having to crystallise them. We’re approaching this “single molecule” diffractive imaging with experiments on ever smaller protein nanocrystals, as well as fibres (one-dimensional crystals). A big issue is reducing the background signal so that the weak molecular diffraction can be measured. This is spurring new methods to introduce samples in the X-ray beam. When these objects are small enough the diffraction patterns contain far more data than can be recorded if limited just to measurements of counts in Bragg peaks. We have been investigating how diffraction phases may be retrieved from such data via iterative algorithms, without the use of a priori information and without restrictions on resolution.