  We propose a method to substantially improve the signal-to-noise ratio of
lattice correlation functions for bosonic operators or other operator
combinations with disconnected contributions. The technique is applicable for
correlations between operators on two planes (zero momentum correlators) when
the dimension of the plane is larger than the separation between the two planes
which are correlated. In this case, the correlation arises primarily from
points whose in-plane coordinates are close, but noise arises from all pairs of
points. By breaking each plane into bins and computing bin-bin correlations, it
is possible to capture these short-distance correlators exactly while replacing
(small) correlators at large spatial extent with a fit, with smaller
uncertainty than the data. The cost is only marginally larger than averaging
each plane before correlating, but the improvement in signal-to-noise can be
substantial. We test the method on correlators of the gradient-flowed
topological charge density and squared field strength, finding noise reductions
by a factor of $\sim$ 3$-$7 compared to the conventional approach on the same
ensemble of configurations.
