  Ten isolated compact high-velocity clouds (CHVCs) of the type cataloged by
Braun & Burton (1999) have been imaged with the Arecibo telescope and were
found to have a nested core/halo morphology. We argue that a combination of
high-resolution filled-aperture and synthesis data is crucial to determining
the intrinsic properties of the CHVCs. We identify the halos as Warm Neutral
Medium surrounding one or more cores in the Cool Neutral Medium phase. These
halos are clearly detected and resolved by the Arecibo filled-aperture imaging,
which reaches a limiting sensitivity (1 sigma) of N_H about 2x10^17 cm^-2 over
the typical 70 km/s linewidth at zero intensity. The FWHM linewidth of the halo
gas is found to be 25 km/s, consistent with a WNM thermal broadening within
10^4 K gas. Substantial asymmetries are found at high N_H (>10^18.5 cm^-2)
levels in 60% of our sample. A high degree of reflection-symmetry is found at
low N_H (<10^18.5 cm^-2) in all sources studied at these levels. The
column-density profiles of the envelopes are described well by the sky-plane
projection of a spherical exponential in atomic volume density, which allows
estimating the characteristic central halo column density, N_H(0) =
4.1+/-3.2x10^19 cm^-2, and characteristic exponential scale-length,
h_B=420+/-90 arcsec. For plausible values of the thermal pressure at the
CNM/WNM interface, these edge profiles allow distance estimates to be made for
the individual CHVCs studied here which range between 150 and 850 kpc.
(abridged)
