The optimum parameters and properties of a new type of neutron monochromator based on elastically bent silicon single crystals are theoretically evaluated. The use of a fully asymmetrical geometry permits the achievement of rocking-curve widths exceeding 20' in the incident beam. The associated effect of the reflected-beam widening is compensated for by the second crystal in the parallel (1,−1) setting in opposite geometry. Reflectivity calculations indicate that this double-crystal system might be compared with the best single-crystal mosaic monochromators. Besides the easy control of the effective mosaicity and the corresponding integrated reflectivity by variation of the bending radius, a further advantage of this system is its simultaneous action as a neutron filter improving the ratio of the thermal neutron signal to the background.