  We confirm and discuss recently discovered cold HI clouds with column
densities among the lowest ever detected. The column densities of Cold Neutral
Medium (CNM) towards 3C286 and 3C287 are ~10^18 cm^-2, below an observational
lower limit, and also below tiny-scale-atomic clouds detected by VLBI and
time-variable profiles against pulsars. These column densities are close to the
minimum imposed by thermal evaporation. The fractions of the CNM to total HI
towards 3C286 and 3C287 are ~4% and <2%, respectively. We discuss the CNM
fraction and the CNM clouds in relation to several theoretical models.
