We previously reported the synthesis and structural characterization of a model membrane protein comprised of an amphiphilic 4-helix bundle peptide with a hydrophobic domain based on a synthetic ion channel and a hydrophilic domain with designed cavities for binding the general anesthetic halothane. In this work, we synthesized an improved version of this halothane-binding amphiphilic peptide with only a single cavity and an otherwise identical control peptide with no such cavity, and applied x-ray reflectivity to monolayers of these peptides to probe the distribution of halothane along the length of the core of the 4-helix bundle as a function of the concentration of halothane. At the moderate concentrations achieved in this study, approximately three molecules of halothane were found to be localized within a broad symmetric unimodal distribution centered about the designed cavity. At the lowest concentration achieved, of approximately one molecule per bundle, the halothane distribution became narrower and more peaked due to a component of ∼19Å width centered about the designed cavity. At higher concentrations, approximately six to seven molecules were found to be uniformly distributed along the length of the bundle, corresponding to approximately one molecule per heptad. Monolayers of the control peptide showed only the latter behavior, namely a uniform distribution along the length of the bundle irrespective of the halothane concentration over this range. The results provide insight into the nature of such weak binding when the dissociation constant is in the mM regime, relevant for clinical applications of anesthesia. They also demonstrate the suitability of both the model system and the experimental technique for additional work on the mechanism of general anesthesia, some of it presented in the companion parts II and III under this title.