  Recently, we provided a simple but accurate formula which closely
approximates the first crossing distribution associated with random walks
having correlated steps. The approximation is accurate for the wide range of
barrier shapes of current interest and is based on the requirement that, in
addition to having the right height, the walk must cross the barrier going
upwards. Therefore, it only requires knowledge of the bivariate distribution of
the walk height and slope, and is particularly useful for excursion set models
of the massive end of the halo mass function. However, it diverges at lower
masses. We show how to cure this divergence by using a formulation which
requires knowledge of just one other variable. While our analysis is general,
we use examples based on Gaussian initial conditions to illustrate our results.
Our formulation, which is simple and fast, yields excellent agreement with the
considerably more computationally expensive Monte-Carlo solution of the first
crossing distribution, for a wide variety of moving barriers, even at very low
masses.
