While testing the new simTBX diffraction image simulator Aaron and I found that some rather beautiful-looking images still won't index. Subsequently, I followed up with mosflm, which does succeed in these cases, even without prior knowledge of the cell or space group.
I have now run this 1000 times, varying only the crystal orientation, and found 171 cases of dials.stills_process failing to index the simulated image whereas mosflm had no trouble, and 5 cases where mosflm failed and dials.stills_process succeeded. There were no overlapping cases where both programs failed.