A detailed description is given of a new facility for transmission 57Fe Mössbauer spectroscopy (MS) studies on absorbers in a miniature diamond-anvil cell in the temperature range 10-300 K and pressure range 0-45 GPa. Spectra with an adequate signal-to-noise ratio for a reliable analysis to be made have each been measured in 20-30 h of data accumulation time. This has been accomplished in spite of the severe constraints imposed by both the minute sample area and the high attenuation of the 14.4 keV probing radiation by the diamond anvils compared with the experimental conditions of conventional MS experiments. A custom-made Rh(57Co) "point" source with a high specific activity has been used in conjunction with absorbers that have an optimal enrichment (10%-20%) of 57Fe. The successful implementation of 57Fe Mössbauer spectroscopy at very high pressures and variable cryogenic temperatures has been accomplished by making relatively simple refinements to existing elements of high-pressure MS methodology.