X-ray diagnostics in today's high-energy density environments must contend with intense and energetic X-ray background levels. In this work, we address the issues of X-ray fluorescence and scattering in reflection-geometry X-ray crystal spectrometers. In this geometry, the detector can capture not only a dispersed X-ray spectrum but also fluorescence and/or scattered X-rays from the diffracting crystal and crystal mounts. Studies to optimally reduce these sources of spectral contamination have been performed using the HENEX spectrometer. Variables that mitigate such unwanted background include filtration, collimation and judicious selection of crystal and detector materials.