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Despite considerable progress over the past years, the detection of medium-energy X-ray photons (E>1 keV) with STJs near the energy-resolution limit, set by the Fano and tunnel noise, remains an elusive goal. There is presently little doubt that the spatially inhomogeneous response of the STJ is responsible for the degradation of the energy resolution. We review several proposed mechanisms against experimental data for Nb- and Ta-based STJs, of various sizes and in single or array-format. We argue against a single mechanism behind the resolution degradation. The experimental results presented here support a model in which quasi-particles are lost at the edges of the STJ, but also indicate that losses into the leads seriously degrade the energy resolution. Finally, an example is given of how fabrication details may play a role as well.