  Conditional cumulants form a set of unique statistics which represent a
sensible compromise between N-point correlation functions and cumulants
measured from moments of counts in cells. They share accurate edge corrected
estimators with $N$-point correlation functions, yet, they are as
straightforward to measure and interpret as counts in cells. The conditional
cumulants have three equivalent views as i) degenerate N-point correlation
functions ii) or integrated monopole moments of the bispectrum iii) they are
closely related to neighbour counts. We compute the predictions of weakly
non-linear perturbation theory for conditional cumulants and compare them with
measurements in simulations, both in real and redshift space. We find excellent
agreement between theory and simulations, especially on scales >~20Mpc. Due to
their advantageous statistical properties and well understood dynamics, we
propose conditional cumulants as tools for high precision cosmology. Potential
applications include constraining bias and redshift distortions from galaxy
redshift surveys
