  We revisit the question of how to calculate correlations of the curvature
perturbation, $\zeta$, using the $\delta N$ formalism when one cannot employ a
truncated Taylor expansion of $N$. This problem arises when one uses lattice
simulations to probe the effects of isocurvature modes on models of reheating.
Working in real space, we use an expansion in the cross-correlation between
fields at different positions, and present simple expressions for observables
such as the power spectrum and the reduced bispectrum, $f_{\rm NL}$. These take
the same form as those of the usual $\delta N$ expressions, but with the
derivatives of $N$ replaced by non-perturbative $\delta N$ coefficients. We
test the validity of this expansion and argue that our expressions are
particularly well suited for use with simulations.
