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A mechanically cooled spectrometer has been constructed and tested separately with Si(Li) planar, high-purity germanium (HPGe) planar, and HPGe coaxial detectors. For each of these types of semiconductor detectors, this spectrometer has attained the lowest noise and best resolution at 5.9 keV, 122 keV, or 1.33 MeV of any closed-cycle mechanically cooled spectrometer which has been reported on in the literature. Resolutions at 5.9 keV were 175 eV FWHM with a 4 mm diameter Si(Li) detector and 202 eV with a 16 mm HPGe planar detector. With a 10% relative efficiency HPGe coaxial detector, resolutions of 816 eV at 122 keV and 1.70 keV at 1.33 MeV were obtained.