Short and intense x-ray pulses may be used for atomic-resolution diffraction imaging of single biological molecules. Radiation damage and a low signal-to-noise ratio impose stringent pulse requirements. In this Letter, we describe methods for decreasing the damage and improving the signal by encapsulating the molecule in a sacrificial layer (tamper) that reduces atomic motion and by postprocessing the pulse-averaged diffraction pattern to correct for ionization damage. Simulations show that these methods greatly improve the image quality.