  We present a new method for embedding a stellar disc in a cosmological dark
matter halo and provide a worked example from a {\Lambda}CDM zoom-in
simulation. The disc is inserted into the halo at a redshift z = 3 as a
zero-mass rigid body. Its mass and size are then increased adiabatically while
its position, velocity, and orientation are determined from rigid-body
dynamics. At z = 1, the rigid disc is replaced by an N-body disc whose
particles sample a three-integral distribution function (DF). The simulation
then proceeds to z = 0 with live disc and halo particles. By comparison, other
methods assume one or more of the following: the centre of the rigid disc
during the growth phase is pinned to the minimum of the halo potential, the
orientation of the rigid disc is fixed, or the live N-body disc is constructed
from a two rather than three-integral DF. In general, the presence of a disc
makes the halo rounder, more centrally concentrated, and smoother, especially
in the innermost regions. We find that methods in which the disc is pinned to
the minimum of the halo potential tend to overestimate the amount of adiabatic
contraction. Additionally, the effect of the disc on the subhalo distribution
appears to be rather insensitive to the disc insertion method. The live disc in
our simulation develops a bar that is consistent with the bars seen in
late-type spiral galaxies. In addition, particles from the disc are launched or
"kicked up" to high galactic latitudes.
