In this paper, we revisit our model-independent methods developed for reconstructing properties of Weakly Interacting Massive Particles (WIMPs) by using measured recoil energies from direct Dark Matter detection experiments directly and take into account more realistically non-negligible threshold energy. All expressions for reconstructing the mass and the (ratios between the) spin-independent and the spin-dependent WIMP-nucleon couplings have been modified. We focus on low-mass (m_chi <~ 15 GeV) WIMPs and present the numerical results obtained by Monte Carlo simulations. Constraints caused by non-negligible threshold energy and technical treatments for improving reconstruction results will also be discussed.
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