Challenges in fabrication and testing have historically limited the choice of surfaces available for the design of reflective optical instruments. Spherical and conic mirrors are common, but, for future science instruments, more degrees of freedom will be necessary to meet performance and packaging requirements. These instruments will be composed of surfaces of revolution located far off-axis with large spherical departure, and some designs will even require asymmetric surface profiles. We describe the design and diamond machining of seven aluminum mirrors: three rotationally symmetric, off-axis conic sections, one off-axis biconic, and three flat mirror designs. These mirrors are for the Infrared Multi-Object Spectrometer instrument, a facility instrument for the Kitt Peak National Observatory’s Mayall Telescope (3.8 m) and a pathfinder for the future Next Generation Space Telescope multi-object spectrograph. The symmetric mirrors include convex and concave prolate and oblate ellipsoids, and range in aperture from 92 x 77 mm to 284 x 264 mm and in f-number from 0.9 to 2.4. The biconic mirror is concave and has a 94 x 76 mm aperture, (formula available in paper) and is decentered by -2 mm in x and 227 mm in y. The mirrors have an aspect ratio of approximately 6:1. The fabrication tolerances for surface error are < 63.3 nm RMS figure error and < 10 nm RMS microroughness. The mirrors are attached to the instrument bench using semi-kinematic, integral flexure mounts and optomechanically aligned to the instrument coordinate system using fiducial marks and datum surfaces. We also describe in-process profilometry and optical testing.