We present the design and simulation of a high resolution inverted time-of-flight option for a neutron spectrometer with crystal analysers in backscattering, with specific reference to the IN16B spectrometer at the Institut Laue-Langevin, Grenoble. While the conventional configuration with Si 111 crystals provides sub-μeV resolution in an energy range limited to ±30 μeV, the novel BATS option (BATS: Backscattering and Time-of-flight Spectrometer) extends the energy window to 340 μeV with only a slightly increased resolution of 1.2 μeV. Moreover, the observation window can be shifted to inelastic energy transfers. To bring this about, a novel fast chopper system with disks of large diameter and complex slit pattern is used, offering high flexibility in resolution and repetition rate. The chopper system consists out of two counter rotating disk chopper pairs. It provides 7 different pulse lengths, three pulse repetition rates up to 237 Hz and can operate with Si 111 or Si 311 crystal analysers. The latter option is a unique feature which covers a Q-range up to 3.7 Å-1 with a resolution of 6.8 μeV. Extensive ray-tracing simulations have been used to validate the design of the pulse chopper system, set limits on the sample size, and assess the achievable energy resolutions of the different chopper configurations.