  Many lattice studies of heavy quark diffusion originate from a
colour-electric correlator, obtained as a leading term after an expansion in
the inverse of the heavy-quark mass. In view of the fact that the charm quark
is not particularly heavy, we consider subleading terms in the expansion.
Working out correlators up to $O(1/M^2)$, we argue that the leading corrections
are suppressed by $O(T/M)$, and one of them can be extracted from a
colour-magnetic correlator. The corresponding transport coefficient is
non-perturbative already at leading order in the weak-coupling expansion, and
therefore requires a non-perturbative determination.
