  In an X-ray reflection spectrum, a tail-like spectral feature generated via
Compton down-scattering, known as a Compton shoulder (CS), appears at the
low-energy side of the iron K$\alpha$ line. Despite its great diagnostic
potential, its use as a spectral probe of the reflector has been seriously
limited due to observational difficulties and modelling complexities. We
revisit the basic nature of the CS by systematic investigation into its
dependence on spatial and temporal parameters. The calculations are performed
by Monte-Carlo simulations for sphere and slab geometries. The dependence is
obtained in a two-dimensional space of column density and metal abundance,
demonstrating that the CS solves parameter degeneration between them which was
seen in conventional spectral analysis using photoelectric absorption and
fluorescence lines. Unlike the iron line, the CS does not suffer from any
observational dependence on the spectral hardness. The CS profile is highly
dependent on the inclination angle of the slab geometry unless the slab is
Compton-thick, and the time evolution of the CS is shown to be useful to
constrain temporal information on the source if the intrinsic radiation is
variable. We also discuss how atomic binding of the scattering electrons in
cold matter blurs the CS profile, finding that the effect is practically
similar to thermal broadening in a plasma with a moderate temperature of
$\sim$5 eV. Spectral diagnostics using the CS is demonstrated with grating data
of X-ray binary GX 301$-$2, and will be available in future with
high-resolution spectra of active galactic nuclei obtained by
microcalorimeters.
