Equation (6) above holds for the standard closure for unclustered networks, but fails to be satisfied for non-zero clustering. The second problem with the standard closure is the question of how triangles of three infected individuals behave during the early asymptotic stage of an epidemic, where all dynamical variables are governed by the proportion of the population that is infectious, (½I=N)%1. While for pure SIS dynamics these triples are not dynamically important, when we come to consider contact tracing similar terms will become relevant. Under (4) and assuming the prevalence of infection is very low, the proportion of unclosed triples composed of three infected individuals is proportional to ½I=N as expected. However, under (4), the proportion of triangles where all three individuals are infected is not small (and does not scale with ½I=N); clearly, this is inconsistent and should be rectified in any improved closure. Motivated by these two considerations, we propose an alternative that respects (6) and has appropriate polynomial dependence on ½I=N during the early epidemic.