In this Letter a fully vectorial numerical model is used to search for the construction parameters of monolithic high-contrast grating (MHCG) mirrors providing maximal power reflectance. We determine the design parameters of highly reflecting MHCG mirrors where the etching depth of the stripes is less than two wavelengths in free space. We analyze MHCGs in a broad range of real refractive index values corresponding to most of the common optoelectronic materials in use today. Our results comprise a complete image of possible highly reflecting MHCG mirror constructions for potential use in optoelectronic devices and systems. We support the numerical analysis by experimental verification of the high reflectance via a GaAs MHCG designed for a wavelength of 980 nm.