<p>Scheme (HEES), a key component of the UK government's Fuel Poverty Strategy. The impact on the fuel poverty gap is simulated using data on a large-scale and representative sample of households in England. The scope for improving the scheme's targeting is considered by examining the optimal allocation of grants between households. The extent to which these potential gains might be achieved in practice using pragmatic criteria for distributing grants, and the implications of taking into account the dynamics of fuel poverty and the self-selection of grant applicants, are also explored. The current scheme is unlikely to have a very significant impact on fuel poverty, and considerable gains could be achieved by redesigning HEES, although the paper also highlights the difficulties involved in efficient targeting, including some additional complications not encountered in the analysis of more traditional anti-poverty measures.</p>