The protein from purple membrane, bacteriorhodopsin, together with lipid, forms two-dimensional membranous arrays of symmetry p3. The protein can also be induced to reform into a planar orthorhombic lattice having at least two slightly different cell dimensions. The p3 and p22₁2₁ (small cell) amplitudes have been combined with the known molecular orientation and envelope to show that it is possible to determine phases to the presently known resolution of 6 Å, with the molecular replacement method. This method was then used to extend phases beyond the present 6 Å resolution limit imposed by low-dose imaging, and to obtain a projection showing the structure of purple membrane protein at 3.3 Å resolution. Data from the p3 structure and both orthorhombic forms were used simultaneously for this extension. The procedure suggests a way of extending the resolution of structures based on electron diffraction data from two-dimensional arrays when the transform can be sampled as finely as desired.