A new data analysis method based on physical observables for WIMP dark matter searches with noble liquid Xe dual-phase TPCs is presented. Traditionally, the nuclear recoil energy from a scatter in the liquid target has been estimated by means of the initial prompt scintillation light (S1) produced at the interaction vertex. The ionization charge (C2), or its secondary scintillation (S2), is combined with the primary scintillation in Log(S2/S1) vs. S1 only as a discrimination parameter against electron recoil background. Arguments in favor of C2 as the more reliable nuclear recoil energy estimator than S1 are presented. The new phase space of Log(S1/C2) vs. C2 is introduced as more efficient for nuclear recoil acceptance and exhibiting superior energy resolution. This is achieved without compromising the discrimination power of the LXe TPC, nor its 3D event reconstruction and fiducialization capability, as is the case for analyses that exploit only the ionization channel. Finally, the concept of two independent energy estimators for background rejection is presented: E2 as the primary (based on C2) and E1 as the secondary (based on S1). Log(E1/E2) vs. E2 is shown to be the most appropriate phase space in which to evaluate WIMP signal candidates.