Diagonal (top) and row (bottom) of the reduced covariance coupling kernels for ℓ ∈ [150, 206, 300, 650, 750] and ∆ = ℓ′ − ℓ = 50 as a function of ∆₂ = ℓ₂ − ℓ. The row (bottom) is plotted for ℓ₁ = ℓ, i.e. ∆₁ = ℓ₁ − ℓ = 0. The plots show that for different I but the same ∆, the kernels are very similar, differing only at the 5% level. A similar result can be shown for other values of ∆. This leads us to formulate our new approximation, where we assume to depend only on the multipole separations ∆, ∆₁, ∆₂.