A sounding rocket payload called the Interstellar Medium Absorption Profile Spectrograph (IMAPS) recorded a spectrum of pi Sco from 1003 to 1172 angstrom with a maximum signal-to-noise ratio of approximately 20 and a velocity resolution of 2.4 km s-1. With our very high spectral resolution, we could distinguish three types of H I as well as two discrete H II regions in velocity space, allowing independent analyses of physical conditions and abundances for the individual gas components. A direct evaluation of optical depths and column densities across the absorption features is applied for the first time to the dominant ionization stage of iron, silicon, and phosphorus. Uncertainties in the laboratory-determined rest wavelengths of various atoms and ions, however, hamper our analysis by creating 1-2 km s-1 ambiguities in the registration of velocities of the different species. We identify one of the H II components with the Stromgren sphere around pi Sco because it shows prominent absorption lines from the excited fine-structure states of N II, while the other appears to be a more diffuse ionized region somewhere along the line of sight to the star. The gas in the Stromgren sphere and in all three H I components appear to be distributed into clumps. As a result, part of the strong Fe II profiles may not have been adequately resolved, despite the high dispersion of our spectrum. The present data not only provide significant new insights into processes that determine the abundances of elements having absorption features in the ultraviolet, but also dramatically improve the interpretation of the ground-based observations of Ca II and Ti II found in the literature. Based in part upon an analysis of our UV spectrum, we conclude that all of the Ti II absorption seen toward pi Sco arises in the warm, neutral intercloud medium (WNM), while the other elements have their maximum absorption associated with cold clouds. Further, a conservative estimate of log sigma < - 3.4 is inferred for the titanium depletion in the cold clouds, a value that is more extreme than any integrated, line-of-sight measurement made to date including the dense sight lines toward zeta Oph, omicron Per, and HD 147889. We derive substantial elemental depletions in all three types of H I gas as well as in the Stromgren sphere. Both Fe II and Si II abundances, relative to that of P II, appear to be approximately 0.3 (dex) more in the WNM than in the cold-cloud component, perhaps suggesting minor amounts of grain destruction. Nevertheless, the element-to-element abundances for the line of sight as a whole are consistent with the results of Joseph or those of Jenkins, Savage, and Spitzer.