The role of the nonlinear processes of interaction of low-energy tightly focused (numerical aperture NA = 0.2) femtosecond pulses, generated by a fiber laser with a repetition rate (0.1–1 MHz), with a solid target placed in air has been analyzed for the first time. It is shown that the effect of generated laser pulses leads to the formation of a low-density zone in the focal surface region, thus minimizing the laser beam self-defocusing when depositing energy to the target and, as a consequence, increasing the radiation intensity as a result of the decrease in the focal spot size to the diffraction limit. A mechanism is proposed, which also makes it possible to increase significantly the X-ray yield upon interaction of intense tandem femtosecond laser pulses with the laser-induced dense surface plasma formed by the tandem prepulse. It is shown that the conditions necessary for reaching a yield of ~8-keV X-ray photons higher than 1010 photons/s can be implemented using a copper target; these characteristics are urgent for designing an efficient microfocus tabletop X-ray source of new generation.