For decades, sulfur has remained underdetected in molecular form within the dense interstellar medium (ISM), and somewhere a molecular sulfur sink exists where it may be hiding. With the discovery of hydrogen peroxide (HOOH) in the ISM in 2011, a natural starting point may be found in sulfur-bearing analogs that are chemically similar to HOOH: hydrogen thioperoxide (HOSH) and hydrogen persulfide (HSSH). The present theoretical study couples the accuracy in the anharmonic fundamental vibrational frequencies from the explicitly correlated coupled cluster theory with the accurate rotational constants provided by canonical high-level coupled cluster theory to produce rovibrational spectra for use in the potential observation of HOSH and HSSH. The ν6 mode for HSSH at 886.1 cm−1 is within 0.2 cm−1 of the gas-phase experiment, and the B0 rotational constant for HSSH of 6979.5 MHz is within 9.0 MHz of the experimental benchmarks, implying that the unknown spectral features (such as the first overtones and combination bands) provided herein are similarly accurate. Notably, a previous experimentally-attributed 2ν1 mode, at 7041.8 cm−1, has been reassigned to the ν1+ν5 combination band based on the present work’s ν1+ν5 value at 7034.3 cm−1. The most intense vibrational transitions for each molecule are the torsions, with HOSH having a more intense transition of 72 km/mol compared to HSSH’s intensity of 14 km/mol. Furthermore, HOSH has a larger net dipole moment of 1.60 D compared to HSSH’s 1.15 D. While HOSH may be the more likely candidate of the two for possible astronomical observation via vibrational spectroscopy due to the notable difference in their intensities, both HSSH and HOSH have large enough net dipole moments to be detectable by rotational spectroscopy to discover the role these molecules may have as possible molecular sulfur sinks in the dense ISM.