Sensitive CO observations are presented for a sample of elliptical gal
axies which are luminous X-ray and weak far infrared (FIR) emitters. O
nly non-detections were obtained. The absence of detectable amounts of
CO (this includes the previously 'detected' prototypical galaxy NGC 4
472) does not support those standard cooling flow scenarios in which d
ust grain sputtering reduces the FIR luminosity, while cooled down sas
is forming a significant mass of dense molecular gas.