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X-pinch plasmas are known as point-like X-ray sources with the potential application for backlighting diagnostics. X-pinches are commonly driven by large pulsed power generators delivering high-voltage pulses with short rise-times, typically under 100 ns. When operating with slower capacitor banks, X-pinches become less reliable because of the arising X-ray pulse jitter and because of the appearance of two or more X-ray bursts coming from multiple hot spots. In this paper, a very compact inductance-capacitance (LC) generator with the current rise-time of 200 ns was used to drive molybdenum and tungsten wire X-pinches. A single peak, small shot-to-shot jitter emission of X-rays was obtained. Time-integrated penumbral imaging recorded the X-ray source dimension of less than 15 μm in the spectral region above 2.4 keV. The total yield of more than 80 mJ was registered with the radiation pulse duration as short as 1.5 ns. The appearance of single- or multiple-source core structures is discussed in correlation with used wire material and X-pinch torsion angle. The results confirm the possibility of using an X-pinch driven by a fast compact capacitor bank for backlighting applications.