The X-ray photoemission electron microscope (XPEEM) has been shown to be a valuable tool for small-area X-ray absorption fine-structure (XAFS) spectroscopy, and for state-selected imaging. The instrument currently in regular operation on bending-magnet monochromators uses electrostatic optics to create an image of a sample surface in vacuum. The instrument can be operated on a wide variety of X-ray and VUV beamlines, and the spectral resolution is determined by the beamline monochromator. The spatial resolution is determined primarily by the aberrations of the immersion lens accelerating field and the objective lens, although other factors such as surface roughness play an important, though less fundamental role. We have tested the spatial resolution of micro-XAFS with a high quality test object, consisting of a free-standing circular zone plate made of gold. These tests confirm the assessment that chromatic aberration limits the performance of the optics, because of the wide range of kinetic energies of secondary electrons produced in XAFS spectroscopy, and the highly asymmetric intensity distribution of these secondaries. One attempt at solving the chromatic aberration problem is the use of an energy filter, which solves the problem by allowing only a narrow band of electrons to produce an image. We describe an alternative approach, based on chromatic aberration correction, which has great potential for an XPEEM instrument with extremely high transmission, and spatial resolution below 10 nm. We also point out the performance improvements to be expected when XPEEM is adapted to high-throughput undulator beamlines.