  We describe and test a new method for creating initial conditions for
cosmological N-body dark matter simulations based on second-order Lagrangian
perturbation theory (2lpt). The method can be applied to multi-mass particle
distributions making it suitable for creating resimulation, or `zoom' initial
conditions. By testing against an analytic solution we show that the method
works well for a spherically symmetric perturbation with radial features
ranging over more than three orders of magnitude in linear scale and eleven
orders of magnitude in particle mass. We apply the method and repeat
resimulations of the rapid formation of a high mass halo at redshift fifty and
the formation of a Milky-Way mass dark matter halo at redshift zero. In both
cases we find that many properties of the final halo show a much smaller
sensitivity to the start redshift with the 2lpt initial conditions, than
simulations started from Zel'dovich initial conditions. For spherical overdense
regions structure formation is erroneously delayed in simulations starting from
Zel'dovich initial conditions, and we demonstrate for the case of the formation
the high redshift halo that this delay can be accounted for using the spherical
collapse model. In addition to being more accurate, 2lpt initial conditions
allow simulations to start later, saving computer time.
