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In an X-ray reflection spectrum, a tail-like spectral feature generated via Compton downscattering, known as a Compton shoulder (CS), appears at the low-energy side of the iron Kα 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 ~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. [ABSTRACT FROM AUTHOR]