  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.
