We present new models for two low-mass X-ray binaries (LMXB), 4U 1822-371 and V1408 Aql (= 4U 1957+115). The eclipsing LMXB 4U 1822-371 is the prototypical accretion disk corona (ADC) system. We have obtained new time-resolved UV spectroscopy of 4U 1822-371 with the Advanced Camera for Surveys/Solar Blind Channel on the Hubble Space Telescope and new V- and J- band photometry with the 1.3-m SMARTS telescope at Cerro Tololo Inter-American Observatory. We use the new data to construct the UV/optical spectral energy distribution of 4U 1822-371 and its orbital light curve in the UV, V , and J bands. We derive an improved ephemeris for the optical eclipses and confirm that the orbital period is changing rapidly, indicating extremely high rates of mass flow in the system; and we show that the accretion disk in the system has a strong wind with projected radial velocities up to 4400 km s⁻¹. We show that the disk has a vertically extended, optically thick component at optical wavelengths. This component extends almost to the edge of the disk and has a height equal to ~0.5 of the disk radius. As it has a low brightness temperature, we identify it as the optically thick base of the disk wind, not as the optical counterpart of the ADC. Like previous models of 4U 1822-371, ours needs a tall obscuring wall near the edge of the accretion disk, but we interpret the wall as a layer of cooler material at the base of the disk wind, not as a tall, luminous disk rim. V1408 Aql is a black hole candidate. We have obtained new optical photometry of this system in 2008 and 2009 with the Argos photometer on the 2.1-m Otto Struve telescope and optical spectra with the low resolution spectrometer on the Hobby Eberly telescope. From the data we derive an improved optical orbital ephemeris and a new geometric model for the system. The model uses only a simple thin disk without the need for a warped disk or a large disk rim. The orbital variation is produced by the changing aspect of the irradiated secondary star with orbital phase. The new model leaves the orbital inclination unconstrained and allows for inclinations as low as 20 degrees. The spectra is largely featureless continuum with He II and occasionally H[alpha] emission lines, and an absorption line from Na D. The lines are highly variable in strength and wavelength, but the variations do not correlate with orbital phase. / text