Experimental requirements for measuring the structure and coverage of adsorbates in the monolayer regime on single crystals with x-ray standing wavefields are discussed in detail along with a thorough description of the theory. The near-surface region of Cu crystals was probed depth selectively by detecting K as well as L fluorescence as a function of fluorescence escape angle. The effects of crystalline imperfections and of dispersive crystal arrangements on the spatial resolution of standing wave measurements are described. Copper crystals with (111) and (100) surface orientation were used as substrates for electrodeposition of Cd and Tl from an aqueous electrolyte using cyclic voltammetry. Submonolayer amounts of Cd and Tl deposited in the underpotential range were investigated on the emerged electrodes with x-ray standing waves keeping the samples under atmospheric pressure, in air, or in inert atmosphere.