  We have observed that the collisional frequency shift in primary caesium
fountain clocks varies with the clock state population composition and, in
particular, is zero for a given fraction of the |F = 4, mF = 0> atoms,
depending on the initial cloud parameters. We present a theoretical model
explaining our observations. The possibility of the collisional shift
cancellation implies an improvement in the performance of caesium fountain
standards and a simplification in their operation. Our results also have
implications for test operation of fountains at multiple pi/2 pulse areas.
