The recent commissioning of a X-ray free-electron laser triggered an extensive research in the area of X-ray ablation of high-Z, high-density materials. Such compounds should be used to shorten an effective attenuation length for obtaining clean ablation imprints required for the focused beam analysis. Compounds of lead (Z=82) represent the materials of first choice. In this contribution, single-shot ablation thresholds are reported for PbWO4 and PbI2 exposed to ultra-short pulses of extreme ultraviolet radiation and X-rays at FLASH and LCLS facilities, respectively. Interestingly, the threshold reaches only 0.11 J/cm(2) at 1.55 nm in lead tungstate although a value of 0.4 J/cm(2) is expected according to the wavelength dependence of an attenuation length and the threshold value determined in the XUV spectral region, i.e., 79 mJ/cm(2) at a FEL wavelength of 13.5 nm. Mechanisms of ablation processes are discussed to explain this discrepancy. Lead iodide shows at 1.55 nm significantly lower ablation threshold than tungstate although an attenuation length of the radiation is in both materials quite the same. Lower thermal and radiation stability of PbI2 is responsible for this finding.