  We analyzed Chandra X-ray observations of five galaxy clusters whose
atmospheric cooling times, entropy parameters, and cooling time to free-fall
time ratios within the central galaxies lie below 1 Gyr, below 30 keV cm^2, and
between 20 < tcool/tff < 50, respectively. These thermodynamic properties are
commonly associated with molecular clouds, bright H-alpha emission, and star
formation in central galaxies. However, none of these clusters have detectable
H-alpha indicated in the ACCEPT database, nor do they have significant star
formation rates or detectable molecular gas. Among these, only RBS0533 has a
detectable radio/X-ray bubble which are commonly observed in cooling
atmospheres. Signatures of uplifted, high metallicity atmospheric gas are
absent. Despite its prominent X-ray bubble, RBS0533 lacks significant levels of
molecular gas. Cold gas is absent at appreciable levels in these systems
perhaps because their radio sources have failed to lift low entropy atmospheric
gas to an altitude where the ratio of the cooling time to the free-fall time
falls below unity.
