[en] Femtosecond x-ray nanocrystallography exploiting XFEL radiation is an emerging method for protein structure determination using crystals with sizes ranging from a few tens to a few hundreds nanometers. Crystals are randomly hit by XFEL pulses, producing diffraction patterns at unknown orientations. One can determine these orientations by studying the diffraction patterns themselves, i.e. by indexing the Bragg peaks. The number of indexed individual images and the SASE bandwidth are inherently linked, because increasing the number of Bragg peaks per individual image requires increasing the bandwidth of the spectrum. This calls for a few percent SASE bandwidth, resulting in an increase in the number of indexed images at the same number of hits. Based on start-to-end simulations for the baseline of the European XFEL, we demonstrate here that it is possible to achieve up to a tenfold increase in SASE bandwidth, compared with the nominal mode of operation. This provides a route for further increasing the efficiency of protein structure determination at the European XFEL.We illustrate this concept with simulations of lysozyme nanocrystals.