  We compute the dark matter halo mass function using the excursion set
formalism for a diffusive barrier with linearly drifting average which captures
the main features of the ellipsoidal collapse model. We evaluate the
non-Markovian corrections due to the sharp filtering of the linear density
field in real space with a path-integral method. We find an unprecedented
agreement with N-body simulation data with deviations within ~5% level over the
range of masses probed by the simulations. This indicates that the Excursion
Set in combination with a realistic modelling of the collapse threshold can
provide a robust estimation of the halo mass function.
