We discuss the design of a new backscattering spectrometer to be installed at the Cold Neutron Research Facility at the National Institute of Standards and Technology. Si (111) crystals cover both monochromator and analyzer which are spherically bent to a radius of curvature of ~ 2 m to focus the incident and scatterered neutron beams. The bending increases the intrinsic lattice gradient of Si beyond its Darwin limit, resulting in an energy resolution of ~ 0.75 μeV FWHM. The monochromator is Doppler-driven, allowing users access to a dynamic range of ±60 μeV. The elastic Q-range covers 0.15 to 1.8 Å-1. The most novel aspect of this design lies in the incorporation of a phase-space-transform chopper. This device rotates at 4700 rpm while neutrons are Bragg-diffracted from sets of pyrolytic graphite crystals affixed to its periphery. The process enhances the neutron flux at the backscattering energy of 2.08 meV, but at the expense of a larger horizontal divergence. Computer simulations indicate a resultant flux increase of order 3 should be obtained.