  We present numerical studies of dipolar spin ice in the presence of a
magnetic field slightly tilted away from the [111] axis. We find a first-order
transition from a kagome ice to a $\mathbf{q}=$X state when the external field
is tilted toward the $[11\bar{2}]$ direction. This is consistent with the
anomalous critical scattering previously observed in the neutron scattering
experiment on the spin ice material
$\textrm{Ho}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$ in a tilted field [Nat. Phys. 3,
566 (2007)]. We show that this ordering originates from the antiferromagnetic
alignment of spin chains on the kagome planes. The residual entropy of the
kagome ice is fully recovered. Our result captures the features observed in the
experiments and points to the importance of the dipolar interaction in
determining ordered states in the spin ice materials. We place our results in
the context of recent susceptibility measurements on
$\textrm{Dy}_{2}\textrm{Ti}_{2}\textrm{O}_{7}$, showing two features for a
[111] field.
