A new source of slow atoms was recently installed on the caesium fountain CSF2 at PTB. This source allows the short-term instability σ y(1s) of CSF2 to be reduced from 2.5×10-13 to 1.7×10-13. Because of the reduced atom loading time and the higher number of atoms, the collisional shift uncertainty is no longer the largest term in the uncertainty budget. The uncertainty is now dominated by the uncertainty contribution due to the observed microwave power dependence of the output frequency. Measurements with the CSF1 fountain suggest that the longitudinal cavity phase gradients produce the observed frequency shifts at elevated power. For normal operation related shifts in CSF1 are expected to be much less than 1×10-16. Due to the larger cloud size associated with the optical molasses used for cooling in CSF2, the effects of longitudinal phase gradients will be even further suppressed in CSF2.