Rough samples with topography on a scale that is much greater than the micrometer dimensions of the electron interaction volume present an extreme challenge to quantitative electron beam x-ray microanalysis with energy-dispersive x-ray spectrometry. Conventional quantitative analysis procedures for flat, bulk specimens become subject to large systematic errors due to the action of geometric effects on electron scattering and the x-ray absorption path compared with the ideal flat sample. The best practical approach is to minimize geometric effects through specimen reorientation using a multiaxis sample stage to obtain the least compromised spectrum. When rough samples must be analyzed, corrections for geometric factors are possible by the peak-to-local background (P/B) method. Correction factors as a function of photon energy can be determined by the use of reference background spectra that are either measured locally or calculated from pure element spectra and estimated compositions. Significant improvements in accuracy can be achieved with the P/B method over conventional analysis with simple normalization.