  The density field reconstruction technique has been widely used for
recovering the Baryon Acoustic Oscillation (BAO) feature in galaxy surveys that
has been degraded due to nonlinearities. Recent studies advocated adopting
iterative steps to improve the recovery much beyond that of the standard
technique. In this paper, we investigate the performance of a few selected
iterative reconstruction techniques focusing on the BAO and the broadband-shape
of the two-point clustering. We include redshift-space distortions, halo bias,
and shot noise and inspect the components of the reconstructed field in Fourier
space and in configuration space using both density field-based reconstruction
and displacement field-based reconstruction. We find that the displacement
field reconstruction becomes quickly challenging in the presence of
non-negligible shot noise and therefore present surrogate methods that can be
practically applied to a much more sparse field such as galaxies. For a galaxy
field, implementing a debiasing step to remove the Lagrangian bias appears
crucial for the displacement field reconstruction. We show that the iterative
reconstruction does not substantially improve the BAO feature beyond an
aggressively optimized standard reconstruction with a small smoothing kernel.
However, we find taking iterative steps allows us to use a small smoothing
kernel more `stably', i.e., without causing a substantial deviation from the
linear power spectrum on large scales. In one specific example we studied, we
find that a deviation of 13\% in $P( k \sim 0.1h/Mpc)$ with an aggressive
standard reconstruction can reduce to 3-4\% with iterative steps.
