A simplified total reflection X-ray fluorescence (TRXF) technique is proposed for the study of the electrical double layer (EDL) near charged monolayers at the air-water interface. In contrast to the parent NTEF (near total external reflection X-ray fluorescence) method, TRXF uses a fixed angle of incidence (below the critical one) and abandons both "spatial resolution" (which is poor anyway) and "absolute calibration" with the bulk reference. These modifications reduce both the duration of experiments and the complexity of the data treatment by 1-2 orders of magnitude and turn TRXF into a truly simple tool for elemental analysis within the EDL. A few TRXF experiments appear sufficient to disprove the model of simultaneous binding of alkali earth metal cations and inorganic anions to negatively charged phospholipid monolayers as proposed in literature. Direct experimental support was provided to the essential feature of the EDL near highly charged interfaces: The main amount of counterions is concentrated in the thin inner part of the EDL irrespective of the electrolyte concentration in the bulk. A study of the counterion competition for the participation in the EDL of highly negatively charged behenylsulfate (BS) monolayers (resulting from packing density limitations) revealed that univalent Cs+ is quite competitive with divalent Ca2+ and Ba2+ (which contradicts the classical Gouy-Chapman model). If the univalent/divalent ion ratio in bulk is 9:1, the corresponding ratio in the EDL is ca. 1.5 for Cs+/Ca2+ and 0.5 for Cs+/Ba2+, whereas the model predicts 0.14 only. Bearing in mind packing density limitations, these values are consistent with a series of sizes for hydrated ions: Cs+ < Ba2+ < Ca2+.