We present deep, pointed $^{12}$CO($J=2-1$) observations of three late-type LSB galaxies. The beam-size was small enough that we could probe different environments (HI maximum, HI mininum, star forming region) in these galaxies. No CO was found at any of the positions observed. We argue that the implied lack of molecular gas is real and not caused by conversion factor effects. The virtual absence of a molecular phase may explain the very low star formation rates in these galaxies.