Two new accelerator target and neutron filter concepts are proposed for boron neutron capture therapy (BNCT) to enable production efficiencies for epithermal neutrons (i.e., neutrons leaving the treatment port and neutrons generated in the target) of ~5 to 10%. These efficiencies are much greater than in previous designs and allow BNCT facilities to use near-term, low-current (~5 mA) proton accelerators. Two target/filter designs are described and their neutronic performance analyzed. In NIFTI-1, epithermal neutrons (maximum energy of ~100 keV) are generated by a proton beam that is maintained slightly above the 1.889-MeV threshold for the 7Li(p,n)7Be reaction. As the proton beam passes through the DISCOS target, which consists of a sequential series (e.g., total of 80) of very thin (several microns) liquid-lithium films on ultrathin rotating beryllium metal foils, the protons are reaccelerated by an applied direct-current field between the foils. This reacceleration enables a high total neutron yield, ~10-4 neutrons/proton. The NIFTI-1 neutron filter, a highly scattering cross-section layer of iron-magnesium, located between the target and the treatment port, impedes neutron transmission for energies >24 keV, but it has a deep window in the scattering cross section at 24 keV. Scattering in the filter and an accompanying thin (~1 cm) hydrogenous neutron "downshifter" yield a neutron output beam with an average energy of ~10 to 20 keV. In the NIFTI-2 design, a single thick lithium target is used, with a proton beam energy (~2.5 MeV) well above the (p,n) threshold. Although the neutron yield from the target is high, ~10-4 neutrons/proton, their energy is much greater (maximum of ~800 keV) than in NIFTI-1. The high-energy neutrons inelastically scatter in a fluorine-containing material (BeF2/PbF2) placed between the target and the NIFTI filter. The neutron beam out of the treatment port has an average energy of ~30 keV. The effectiveness of the two designs for BNCT treatment is analyzed. Both exhibit good penetration in tissue (advantage depth) and tumor/healthy tissue dose (relative biological effectiveness advantage ratio) performance.