  A simple criterion to optimise coarse-grainings for exact renormalisation
group equations is given. It is aimed at improving the convergence of
approximate solutions of flow equations. The optimisation criterion is generic,
as it refers only to the coarse-grained propagator at vanishing field. In
physical terms, it is understood as an optimisation condition for amplitude
expansions. Alternatively, it can be interpreted as the requirement to move
poles of threshold functions away from the physical region. The link to
expansions in field amplitudes is discussed as well. Optimal parameters are
given explicitly for a variety of different coarse-grainings. As a by-product
it is found that the sharp cut-off regulator does not belong to the class of
such optimal coarse-grainings, which explains the poor convergence of amplitude
expansions based on it.
