A lower limit to the distance of the high-velocity cloud (HVC) complex A of 4 kpc (z > 3 kpc) is derived. The HVC is detected toward the Seyfert galaxy Mrk 106 in Mg n ΛΛ2796, 2803 absorption spectra taken with Hubble Space Telescope (HST) proving that Mg+ is present in the cloud. It is not detected in the Mg ii spectra of two stars, PG 0859 + 593 (distance 4 kpc) and PG 0906 + 597 (distance 0.7 kpc). The distances to the stars are derived by matching Stromgren photometry and intermediate-resolution spectroscopy with model stellar atmospheres; they are estimated to be accurate to within 1 kpc. From a combination of Effelsberg data and Westerbork maps with 2' or 3' resolution, we show that the H i column density and thus the Mg+ abundance in the direction of the two stars is sufficiently high for the nondetections to imply that the HVC is behind the stars. This distance limit can be used to eliminate several recent models for complex A that placed it nearby.We also derive a distance bracket of 1.7 < d < 4 kpc (1.1 < z < 3 kpc) for an intermediate-velocity cloud (IVC) at velocities of about –50 km s–1. This IVC was named the Low-Latitude Intermediate-Velocity Arch by Kuntz & Danly and is seen between l = 120°-160° and b = 30°-45°.