Abstract
Sensitive CO observations are presented for a sample of elliptical galaxies which are luminous X-ray and weak far infrared (FIR) emitters. Only non-detections were obtained. The absence of detectable amounts of CO (this includes the previously 'detected' prototypical galaxy NGC 4472) does not support those standard cooling flow scenarios in which dust grain sputtering reduces the FIR luminosity, while cooled down sas is forming a significant mass of dense molecular gas.