The high- and intermediate-velocity interstellar clouds (HVCs/IVCs) are tracers of energetic processes in and around the Milky Way. Clouds with near-solar metallicity about 1 kpc above the disk trace the circulation of material between disk and halo (the Galactic fountain). The Magellanic Stream consists of gas tidally extracted from the SMC, tracing the dark matter potential of the Milky Way. Several other HVCs have low metallicity and appear to trace the continuing accretion of infalling intergalactic gas. These assertions are supported by the metallicities (0.1 to 1 solar) measured for about 10 clouds in the past decade. Direct measurements of distances to HVCs have remained elusive, however. In this paper we present four new distance brackets, using VLT observations of interstellar Ca II H and K absorption toward distant Galactic halo stars. We derive distance brackets of 5.0 to 11.7 kpc for the Cohen Stream (likely to be an infalling low-metallicity cloud), 9.8 to 15.1 kpc for Complex GCP (also known as the Smith Cloud or HVC 40-15+100 and with still unknown origin), 1.0 to 2.7 kpc for an IVC that appears associated with the return flow of the fountain in the Perseus arm, and 1.8 to 3.8 kpc for cloud g1, which appears to be in the outflow phase of the fountain. Our measurements further demonstrate that the Milky Way is accreting substantial amounts of gaseous material, which influences the Galaxy's current and future dynamical and chemical evolution.Based on observations carried out at the European Southern Observatory (ESO), La Silla, under program ID 077.B-0359 (PI: P. Richter) with the UVES at the ESO Very Large Telescope, Paranal, Chile.