  We study the three-dimensional Kasteleyn transition in both nearest
neighbours and dipolar spin ice models using an algorithm that conserves the
number of excitations. We first limit the interactions range to nearest
neighbours to test the method in the presence of a field applied along $[100]$,
and then focus on the dipolar spin ice model. The effect of dipolar
interactions, which is known to be greatly self screened at zero field, is
particularly strong near full polarization. It shifts the Kasteleyn transition
to lower temperatures, which decreases $\approx 0.4 K$ for the parameters
corresponding to the best known spin ice materials, $Dy_2Ti_2O_7$ and
$Ho_2Ti_2O_7$. This shift implies effective dipolar fields as big as $0.05$
tesla opposing the applied field, and thus favoring the creation of "strings"
of reversed spins. We compare the reduction in the transition temperature with
results in previous experiments, and study the phenomenon quantitatively using
a simple molecular field approach. Finally, we relate the presence of the
effective residual field to the appearance of string-ordered phases at low
fields and temperatures, and we check numerically that for fields applied along
$[100]$ there are only three different stable phases at zero temperature.
