We have imaged five compact high-velocity clouds in Hi with arcmin angular resolution and km s 1 spectral reso- lution using the Westerbork Synthesis Radio Telescope. These CHVCs have a characteristic morphology, consisting of one or more quiescent, low-dispersion compact cores embedded in a diuse warm halo. The compact cores can be unambiguously identified with the cool neutral medium of condensed atomic hydrogen, since their linewidths are significantly narrower than the thermal linewidth of the warm neutral medium. Because of the limited sensitivity to diuse emission inherent to interfer- ometric data, the warm medium is not directly detected in the WSRT observations. Supplementary total-power data, which is fully sensitive to both the cool and warm components of Hi, is available for comparison for all the sources, albeit with angular resolutions that vary from 3 0 to 36 0 . The fractional Hi flux in compact CNM components varies from 4% to 16% in our sample. All objects have at least one local peak in the CNM column density which exceeds about 10 19 cm 2 when observed with arcmin resolution. It is plausible that a peak column density of 1-2 10 19 cm 2 is a prerequisite for the long-term survival of these sources. One object in our sample, CHVC 120 20 443 (Davies' cloud), lies in close projected proximity to the disk of M 31. This object is characterized by exceptionally broad linewidths in its CNM concentrations, more than 5 times greater than the median value found in the 13 CHVCs studied to date at comparable resolution. These CNM concentrations lie in an arc on the edge of the source facing the M 31 disk. The diuse Hi component of this source, seen in total-power data from the NRAO 140-foot telescope, has a positional oset in the direction of the M 31 disk. All of these attributes suggest that CHVC 120 20 443 is in a dierent evolutionary state than most of the other CHVCs which have been studied. Similarly broad CNM linewidths have only been detected in one other cloud, CHVC 110.6 07.0 466 (Wakker & Schwarz 1991) which also lies in the Local Group barycenter direction and has the most extreme radial velocity known. A distinct possibility for Davies' cloud seems to be physical interaction of some type with M 31. The most likely form of this interaction might be the ram-pressure or tidal-stripping by either one of M 31's visible dwarf companions, M 32 or NGC 205, or else by a dark com- panion with an associated Hi condensation. The compact objects located in the direction of the Local Group barycenter have an important role to play in constraining the Local Group hypothesis for the deployment of CHVCs.