We confirm and discuss recently discovered cold H I clouds with column densities among the lowest ever detected. The column densities of the cold neutral medium (CNM) toward 3C 286 and 3C 287 are ~1018 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 ratios of the CNM to total H I toward 3C 286 and 3C 287 are ~4% and 2%, respectively. We discuss the CNM fraction and the CNM clouds in relation to several theoretical models.
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